Creatures in DF currently tend to get "bled to death" when set on fire or bathing in magma. This is due to the melting body fat-related tissue bleeding.
If you remove the ability to bleed (or creature has no fat?), creatures tend to get "died in the heat" when exposed to high temperatures, or "frozen to death" when exposed to low temperatures. This happens when the creature's THOUGHT body parts (i.e. brain) accumulate damage (tracked through unit wounds) due to temperature relative to the brain material's HEATDAM_POINT or COLDDAM_POINT. Creatures that don't have or don't need a THOUGHT body part can't die this way, but can die if their head/upperbody/lowerbody is melted. In theory the game should kill gas or liquid creatures that condense/solidify/boil, but most of those creatures have fixed temperatures.
If you remove the ability to bleed and give brain materials [HEATDAM_POINT:NONE], but still have an IGNITE_POINT, creatures should get "burned to death" when the brain accumulates fire damage. Please note that fire damage != heat damage in DF. Heat and cold damage can grow very quickly, depending on the magnitude of the temperature difference, but fire damage grows over time after the body part has ignited.
DF ought to kill creatures that lose heart function (i.e. frozen solid), but as-is the heart is simply a weak point for bleeding to death. DF does not model heatstroke/hypothermia, and it may be difficult to implement in the current system. Water boils at 10180 U, and the brain doesn't take heat damage until 10250 U!
I suppose some modders can find interesting ways to use this information.
EDIT:
When taking heat damage you are:
blistering
burning
being incinerated
When taking cold damage you are:
freezing
being frozen solid <= (this has nothing to do with the melting point!)
freezing to death
When taking fire damage you are:
on fire
burning alive
burning to death