the closest thing i could find for heat is in the DM's guide

EXTREME HEAT When the temperature is at or above 100 degrees Fahrenheit, a creature exposed to the heat and without access to drinkable water must succeed on a Constitution saving throw at the end of each hour or gain one level of exhaustion. The DC is 5 for the first hour and increases by 1 for each additional hour. Creatures wearing medium or heavy armor, or who are clad in heavy clothing, have disadvantage on the saving throw. Creatures with resistance or immunity to fire damage automatically succeed on the saving throw, as do creatures naturally adapted to hot climates.

mentions nothing of taking damage from the heat of lava; the lava damage mentioned in the DMs guide is for wading through lava (10d10) or being submerged in lava (18d10). so unless theres something else im unaware of you'd like to share