Leomund’s Tiny Hut says
Creatures and objects within the dome when you cast this spell can move through it freely. All other creatures and objects are barred from passing through it. Spells and other magical Effects can't extend through the dome or be cast through it. The Atmosphere inside the space is comfortable and dry, regardless of the weather outside.
Wall of Fire says
When the wall appears, each creature within its area must make a Dexterity saving throw. On a failed save, a creature takes 5d8 fire damage, or half as much damage on a successful save.
One side of the wall, selected by you when you cast this spell, deals 5d8 fire damage to each creature that ends its turn within 10 feet of that side or inside the wall. A creature takes the same damage when it enters the wall for the first time on a turn or ends its turn there. The other side of the wall deals no damage.
Does Tiny Hut negate the magical heat of Wall of Fire or does it cook the adventurer?
Best Answer
Magical effects can’t extend through the dome.
If the wall of fire is on the outside, it doesn’t affect creatures on the inside because Leomund's tiny hut says:
First, the damage from the wall of fire is a magical effect that cannot pass through the dome. Second, the dome doesn’t care about the temperature outside, “the space is comfortable and dry, regardless of the weather outside.”
If for some reason you cast wall of fire while inside the dome, you’re in for a bad time.
This is a bad idea. The clause in the spell description about it being comfortable inside the dome only applies when you don’t change that by doing something like casting wall of fire inside the dome.
If you do happen to find yourself on the wrong side of a wall of fire that was cast inside the dome, you will take the damage.