All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is incumbent on the man in reference to fulfill his vow if he can; Allah, The Exalted, says (what means): {Then let them end their untidiness and fulfill their vows and perform Tawaaf [circumambulation] around the ancient House."} [Quran 22:29] Moreover, the Prophet, sallallahu ‘alayhi wa sallam, said, "Whoever vows to obey Allah, let him obey Him, and whoever vows to disobey Allah, let him not (fulfill his vow and) disobey Him." [Al-Bukhari]
The intense heat does not prevent fasting in an absolute way, as the fasting person may remain in the shade and use air conditioners and the like. Also, the relatively long daytime does not prevent fasting; the fasting person may overcome this problem with having a late pre-dawn meal (Sahoor). Indeed, the pre-dawn meal abounds in great blessings, as was authentically reported in the hadeeth (and it helps to provide the needed energy during the long hours of fasting).
If the person in reference is able to fast, then he is obliged to do so in order to fulfill his vow. However, if he is unable to fast because fasting would cause him an unbearable hardship due to the long daytime or the intense heat from which he cannot protect himself and he knows that he has no hope of overcoming his inability to fast, then he is obliged to make an expiation for breaking his vow.
Ibn ‘Abbaas, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, said, "...whoever makes a vow and is not able to fulfill it, the expiation for that is the expiation for breaking an oath, and whoever makes a vow and is able to fulfill it, then let him do so." [Abu Daawood and others]
The expiation for breaking an oath is to feed or clothe ten poor persons or free a slave. If one cannot afford this, then he should fast three days, and it is better to fast them consecutively because some scholars held that the expiation for breaking an oath requires succession. For more benefit, please refer to fatwa 102811.
Allah knows best.