Is it permissible for a person who is living in a state of unhappiness and deprivation, suffering from intense lust, and unable to afford the costs of marriage, to contract a mut'ah marriage or a temporary marriage that ends after several months?

Be reassured and beware of despairing of Allah's mercy, for it is one of the gravest sins and a characteristic of disbelievers. Indeed, His mercy encompasses all things, and He accepts the repentance of those who repent. Happiness is not in the abundance of wealth, but in faith, contentment, and satisfaction. This world is more insignificant to Allah than we can imagine. Your discontent with your situation is due to your not remembering Allah's blessings upon you, such as sight, hearing, and health. Joy and delight are found in turning to Allah and obeying Him. "Whoever does righteousness, whether male or female, while he is a believer - We will surely cause him to live a good life," and whoever turns away from the remembrance of Allah will have a constricted life. Any worry or sorrow that afflicts a believer is an expiation for their sins by Allah's mercy. Mut'ah marriage (temporary marriage) is invalid and forbidden, and marriage with the intention of divorce is also invalid according to the majority. The correct way is marriage with the intention of permanence and continuation.