Is the covering of one's nakedness considered fulfilled in prayer if the 'awrah is not visible to those around me, yet it is uncovered when viewed from beneath the garment, knowing that this necessity to lighten clothing is due to intense heat?

Concealing the 'awrah (private parts) during prayer is obligatory and a condition for its validity. This is done by covering it with something that does not reveal the skin color. If the garment is thin, allowing the skin color to be seen through it, then prayer in it is not permissible. The intention is not that the 'awrah should not be seen from below, but rather that it should not be seen by those beside you, as evidenced by the fact that the Salaf (pious predecessors) used to wear izars (waist wraps). One must be careful not to wear anything that reveals the skin color during bowing (ruku') and prostration (sujud), for it invalidates the prayer.