The hadithic and Quranic reasoning for the permissibility and validity of temporary marriage is so much that no one can deny it and say that they are all unauthentic or forged. Of course, it can be concluded from the whole of these hadiths that one who isn't married or is but whose wife isn't reachable are the ones being addressed by hadiths that encourage temporary marriage and say it is mustahabb, and it can't be proven that these hadiths are also addressing those who are married and in no need of it.
In order to get the answer to this question, two subjects need to be analyzed:
1- The permissibility of temporary marriage according to the Quran and traditions
Here we will first list the Quranic verses on the subject and then the traditions
a) The Quran and temporary marriage
Concerning the permissibility of temporary marriage, this verse can be referred to: “…For the enjoyment [throught temporary marriage] you have had from them thereby, give them their dowries, by way of settlement, and there is no sin upon you in what you may agree upon after the settlement. Indeed Allah is all-knowing, all-wise”
Allamah Tabatabai interprets this verse like so: “Without a doubt, what is meant by “enjoyment” in the verse, is temporary marriage, because the verse was revealed in Medinah which can be found out by the fact that surah Nisa in which this verse is located in has been revealed in Medinah. This surah has been revealed in the first half of the time period after the migration of the prophet (pbuh) and most of its verses corroborate this matter. [As was said,] this verse is speaking of temporary marriage, something very common and normal during that time that there is no doubt about. Therefore, there is no doubt about the fact that this type of marriage would take place in the presence of the prophet (pbuh) [and he wouldn’t forbid it], also, there is no doubt that in those times, this marriage was referred to with the same name that we use to refer to which is “Mut’ah”, therefore, one has no choice but to admit that when the verse says: “فما استمعتم به منهن” and uses a derivative of the word Mut’ah, it is referring to temporary marriage, the same way the Quran refers to other traditions of the Arabs in that time using the same names they would use. If a verse wanted to speak of the ruling on one of those traditions, or wanted to command or forbid it, it had no other way but to name it using the same name they were familiar with and the people of that time had no other choice but to understand what the name referred to in their culture, not its literal meaning that usually had almost nothing to do with what it was referring to. For example, the words “Hajj”, “Bey’”, “Riba”, “Ribh” and “Ghanimah” all have a literal meaning that can be found in the dictionary, and at the same time, refer to other things as well. For instance, the word Hajj literally means “to intend”, nevertheless, its famous meaning amongst the Arabs of that time was the well-known pilgrimage and circulation around the Ka’bah, and it is impossible for one to claim that when the Quran speaks of “Hajj”, it is speaking of intending something; the same goes for the names and titles the prophet (pbuh) would use, such as “Salat”, “Zakat”, “Hajj Tamattu’” and the like which all had their own literal meanings before being used for others, or being used for a specific instance of the original meaning (like “salat” which originally meant supplication, but was later used for a certain instance and form of supplication which is the prayer performed by Muslims). It was used to refer to this prayer so much to the extent that whenever it was mentioned, the first thing that came to mind was the prayer, not supplication. Therefore, after such a thing takes place, we can no longer say that the literal meaning of these words and names are what is meant when they are used (one of those names being the Mut’ah, which literally means enjoyment, but was used to refer to temporary marriage then).”
b) Hadith sources and Mut’ah
All Shia hadith sources, including the four most authentic ones which are referred to as the “Kutub Arba’” (The Four Books) all have separate chapters for Mut’ah and its permissibility, namely:
1- Kitab Kafi
2- Kitab Man La Yahduruhul-Faqih
There are also many other Shia sources that can't be denied.
In addition to the Quran, the hadiths on this subject are so much that they leave no room for any doubt about their authenticity. Some of them are as follows:
1- Imam Baqir (as) narrates Imam Ali (as) saying: “If Umar (ibn Khattab) hadn’t come before me (and made Mut’ah haram) only the evil and stone-hearted would commit adultery (because they are the only ones who would perform a haram act when the halal form is right there).”
2- One of the companions of Imam Musa Kadhim (as) says: “I told the imam (as) that I used to contract the temporary marriage much, but then I felt like it was something bad and immoral and the people would also scold me for it, all of this led to me vowing to Allah (swt) between the “pillar” and “standing place” (beside the Ka’bah which one of the holiest places) not to practice such a thing again!” The imam (as) replied: “You have vowed to Allah (swt) not to obey Him! By God if you do not obey Allah (swt), you will verily sin and disobey Him.”
Keeping in mind what was said, one can conclude with certainty that the permissibility and being mustahabb of Mut’ah is something that one can't doubt in, although there are some forged false hadiths that may say otherwise. For further information, see: Question 844 (website: 915) The Permissibility of temporary marriage.
2- The boundaries and limits of temporary marriage
Concerning the boundaries and limits of temporary marriage and the number of “temporary wives” one can have, one must say: Although there are authentic hadiths that tell us there is no limit to the number of temporary wives one can have, yet considering the origin and cause of these hadiths and also taking into consideration all of the hadiths regarding temporary marriage as a whole, it can be said that there are certain limits to temporary marriage. In our hadith sources, there are chapters by the name of “The Kirahah (being makruh) of Mut’ah for one who isn't in need of it”, meaning that it is makruh for one who has a “permanent wife” and consequently doesn’t need temporary marriage to contract it. Here we will mention a hadith that can be found in Usul Kafi, one of the most authentic Shia sources compiled by Muhammad ibn Yaqub Kuleini:
A person by the name of Fat’h ibn Yazid reports that he asked Imam Musa Kadhim (as) about Mut’ah, the imam (as) replied: “It is halal and permissible for one whom Allah (swt) hasn’t made needless of permanent marriage and looks to temporary marriage in order to observe chastity and modesty. But if one has become needless of temporary marriage as a result of having married (permamently), Mut’ah will only be permissible if his wife isn't with him (like when he is travelling and he is afraid that he will commit sin if he doesn’t).”
It becomes clear from hadiths like these that temporary marriage can be done when one isn't married and wants to stay away from sin. As for the istihbab (being mustahabb) of temporary marriage for those who are married and whose wives are present, thus aren't in any need of it, it is something that can't be proven. [Therefore, it can't be said that it is mustahabb even for these individuals, although it is still permissible because of other hadiths that disclose its permissibility even for them.]
 فَمَا اسْتَمْتَعْتُمْ بِهِ مِنْهُنَّ فَآتُوهُنَّ أُجُورَهُنَّ فَرِیضَةً وَ لا جُناحَ عَلَیْکُمْ فِیما تَراضَیْتُمْ بِهِ مِنْ بَعْدِ الْفَرِیضَةِ إِنَّ اللَّهَ کانَ عَلِیماً حَکِیما Nisa:24.
 Seyyid Muhammmad Husein Tabatabai, Al-Mizan fi Tafsiril-Quran, vol. 4, pp. 271 and 272.
 Thiqatul-Islam Kuleini, Al-Kafi (8 volumes), vol. 5, pp. 448-465.
 Sheikh Saduq, Man La Yahduruhul-Faqih, vol. 3, pp. 458-467.
 Sheikh Tusi, Al-Istibsar, vol. 3, pp. 141-155.
 Sheikh Hurr Ameli, Wasa’ilul-Shia, vol. 21, pp. 5-81.
 Muhaddith Nouri, Mustadrakul-Wasa’il, vol. 14 (chapters on Mut’ah), pg. 447.
 Muhaddith Nouri, Mustadrakul-Wasa’il, vol. 14, pg. 453.
 Thiqatul-Islam Kuleini, Al-Kafi, vol. 5, pg. 451.
 For further information, see: Question 3320 (website: 4098) The Analysis of the Hadiths on Mut’ah.
 1- عَلِیُّ بْنُ إِبْرَاهِیمَ عَنْ أَبِیهِ عَنِ ابْنِ أَبِی عُمَیْرٍ عَنْ عَلِیِّ بْنِ یَقْطِینٍ قَالَ سَأَلْتُ أَبَا الْحَسَنِ مُوسَى ع عَنِ الْمُتْعَةِ فَقَالَ وَ مَا أَنْتَ وَ ذَاکَ فَقَدْ أَغْنَاکَ اللَّهُ عَنْهَا قُلْتُ إِنَّمَا أَرَدْتُ أَنْ أَعْلَمَهَا فَقَالَ هِیَ فِی کِتَابِ عَلِیٍّ ع فَقُلْتُ نَزِیدُهَا وَ تَزْدَادُ فَقَالَ وَ هَلْ یَطِیبُهُ إِلَّا ذَاکَ.
2- عَلِیُّ بْنُ إِبْرَاهِیمَ عَنِ الْمُخْتَارِ بْنِ مُحَمَّدِ بْنِ الْمُخْتَارِ وَ مُحَمَّدُ بْنُ الْحَسَنِ عَنْ عَبْدِ اللَّهِ بْنِ الْحَسَنِ الْعَلَوِیِّ جَمِیعاً عَنِ الْفَتْحِ بْنِ یَزِیدَ قَالَ سَأَلْتُ أَبَا الْحَسَنِ ع عَنِ الْمُتْعَةِ فَقَالَ هِیَ حَلَالٌ مُبَاحٌ مُطْلَقٌ لِمَنْ لَمْ یُغْنِهِ اللَّهُ بِالتَّزْوِیجِ فَلْیَسْتَعْفِفْ بِالْمُتْعَةِ فَإِنِ اسْتَغْنَى عَنْهَا بِالتَّزْوِیجِ فَهِیَ مُبَاحٌ لَهُ إِذَا غَابَ عَنْهَا.
Thiqatul-Islam Kuleini, Al-Kafi, vol. 5, pg. 453.