Marriage of pleasure (Muta’h) is one in which a man marries a woman but only for a set period of time and solely for pleasure. 

Marriage of pleasure is forbidden, as the prophet ﷺ forbade it, and it is forbidden in the Quran as well in the saying of Allah SWA when he describes the believers: (And those who guard their private parts, except from their wives or those who their right hand possess, for indeed they will not be blamed, but whoever seeks beyond that, then those are the transgressors). Marriage of pleasure is outside these two boundaries, it exceeds the limits set down by Allah SWA, and its prohibition is clear in the sunnah, and there is no doubt amongst the scholars of hadith and jurisprudence.

As for the Misyar marriage, it is a marriage wherein a man marries a woman legally, fulfilling all the conditions and pillars of marriage, except that he is not bound to provide for her financially or provide her housing. It is a complete legal and correct marriage. There is no harm in it if this is what was agreed upon in the marriage contract, then a man does not have to spend on the wife or provide her housing.