Inspired by this question while figuring out potential ways of circumventing this with an adequately equipped and intelligent enemy.
The thought occurred to me that, whereas you could not send burning pitch through the hut the spell alludes to the temperature within only being comfortable regardless of weather.
The atmosphere inside the space is comfortable and dry, regardless of
the weather outside.
So assume the following: The rogues from the referenced question are besieged by their former comrades in their bandit clan and the bandits take cover to negate their sneak attacks. All the while the bandit leader orders wood to be thrown at the hut eventually making, in essence, a bonfire around the hut or something similar like burning pitch etc.
The hut's intention seems to be to keep you safe from the elements so you don't die from exposure and to protect you at least a little bit from being attacked in your sleep. However, if the heat and oxygen depletion were to occur not from weather, but from an external source, could such an act like, say, a catapult of burning pitch cook them alive in their little castle?
Best Answer
The magic most likely protects the occupants
Bringing real-world physics into the discussion of magic is always risky, and your quote above specifically tells you about what's happening inside the hut: it's comfortable and dry...because magic. The likely intent of Tiny Hut is to create a safe place to spend 8 hours.
As Speedkat says below in comments, if we go by the adage of spells do what they say and no more, then there are no circumstances in which the atmosphere is anything but comfortable and dry because the spell doesn't state that there are.
The idea of ways to make it unsafe by introducing real-world physics into the equation is risky and makes the magical spell seem less powerful. This isn't a physical structure that's created that works within the physical world, it's magic. Let the magic be magical.
This doesn't mean that a DM may rule otherwise, but in general that line states that the interior is a safe place to be no matter what's happening outside of it.
In addition, the easiest counter to Tiny Hut is simply having someone able to come in to Dispel Magic on it.
Commentary: Does this make Leomund's Tiny Hut overpowered?
I do not think it does, mostly because it is very situational. In a typical combat, having at least a minute to cast the spell is highly unlikely. In a scenario where you've got time to prepare, the enemy does as well and there are several obvious ways to counter the tiny hut from a simple cast of dispel magic to treating the hut as a fortress under siege to simply ignoring it and waiting out the time. If your enemy is all camped in one location, there may be multiple other targets that are now vulnerable. Don't take the situational factor of when Tiny Hut does it's job as judgement that it's overpowered.