Atopic dermatitis may be considered here.Your rash
appears to be triggered by heat
and the incidence reverts spontaneously after a few minutes once in a cooler environment.
I suggest that you have this assessed by an allergologist or clinical immunologist. An atopic reaction has to be ruled out.
At this point avoid exposure to extreme heat and take frequent baths to cool the body.You may use mild moisturizers with menthol and camphor for cooling effects .