Does 5e not have anything like "Any character within x feet of this [heat source] at the end of its turn takes y-amount of damage"?Not really worth anything. D&D has rules for fire damage. It doesn't have rules for exposure to heat.
I know some creatures give off enough heat or cold to auto-damage anyone in melee with them, repeating every round.
These are the sort of thing a basic Heat Resistance could really help with.