All Muslims believe that Mutah was an established practice by the Prophet (saw). Historically, it was Caliph Umar who forbade the practice -
"Book 007, Number 2801:
Abu Nadra reported: Ibn'Abbas commanded the performance of Mut'a putting lhram for 'Umra during the months of Dhu'I-Hijja and after completing it. then putting on Ibrim for Hajj), but Ibn Zubair forbade to do it. I made a mention of it to Jabir b. Abdullih and he said: It is through me that this hadith has been circulated.
We entered into the state of Ihram as Tamattu' with the Messenger of Allah (may peace be upon him). When 'Umar was Installed as Caliph, he said: Verily Allah made permissible for His Messenger (may peace be upon him) whatever He liked and as He liked. And (every command) of the Holy Qur'an has been revealed for every occasion. So accomplish Hajj and Umra for Allah as Allah has commanded you; and confirm by (proper conditions) the marriage of those women (with whom you have performed Mut'a).
And any person would come to me with a marriage of appointed duration (Mut'a), I would stone him (to death). Qatada narrated this hadith with the same chain of transmitters saying: (That 'Umar also said): Separate your Hajj from 'Umra, for that is the most complete Hajj, and complete your Umra." [Sahih Muslim, Book 7, Number 2801 and 2814]
Source: Sahih Muslim Online
http://www.usc.edu/org/cmje/religious-texts/hadith/muslim/007-smt.phpAs for the hadith you cited, it's from the book "Minhaj al-Waqifa" which is a book from the sect of Shiism that believes in 7 Imams. This website only deals with Twelver Shiism and their books and beliefs. Your argument is not valid because it comes from a book (al-Wafiqa) that is derived from a sect of Shiism that is nearly dead. Please stick to credible sources.
Finally, your assertion that mutah is not allowed solely for sexual pleasure is incorrect. In Islam, we already have the established principle of relationships solely for sexual pleasure. Two examples.
1) "Slave-women" i.e. women who were captured during wartime. The Qu'ran refers to them as "those who your right hand possesses". A fairly obvious verse that they are for sexual pleasure is the following:
“No woman are permitted to you [the Prophet] in the future, nor is it allowed for you to change your wives for other women, even if there beauty may stun you, except for those whom your right hand possess”.
Al-Qur’an, Surah 33, Ayah 52
By the way, are you aware of the the reason why the verse 4:24 was even revealed? Take a read here:
http://www.qtafsir.com/index.php?option=com_content&task=view&id=684&Itemid=59"Imam Ahmad recorded that Abu Sa`id Al-Khudri said, "We captured some women from the area of Awtas who were already married, and we disliked having sexual relations with them because they already had husbands. So, we asked the Prophet about this matter, and this Ayah was revealed. Consequently, we had sexual relations with these women"
See here? The reason why they initially wanted to marry these women was for sexual pleasure only. They were afraid it was haram because they were already married (to non-Muslim men). This verse was revealed and told them it was okay to have sexual relations with them - not real marriage.
2)The concept of misyar. Qaradawi himself admits that most people who did are already married. He suggests it is a lawful method of fulfilling one's sexual desires without having to fulfill all of the responsibilities a man has towards the woman (i.e. nafaqah). Like Mutah, some have also compared it to prostitution. Why? Because anything in Islam can be abused.
Mutah was permitted by the Prophet and it does have an Islamic basis. Anything can be abused (like misyar).
Mutah is permissible.