For my LO, heat rash will occur usually after shower cause we shower with warm water. If heat rash, can let baby go topless daytime or get those holey singlets, likewise for bottom area, can go diaperless to air dry the area after cleaning.
At night can dress lightly instead of PJ and remove all the pillows/blankets (kids tend to perspire more easily).
I can’t advise if it’s eczema cause we only encountered heat rash before.