TLDR: Braziers continue to produce heat (raise temperature in the room they're in) when they run out of fuel.

My colony has run into a bit of a wood shortage, so everything that was wood dependant ran out of fuel. My wood burning generator, stove, and all my braziers are showing out of fuel, as expected. However, I noticed that in rooms with the Brazier installed, they were still flucuating at 28-29C even though it was 9C outside. As expected they stop functioning as a light source, but they all seem to be producing heat even when out of fuel.

I uninstalled all the braziers and the rooms that had them dropped in temperature to match the outside temperature over time as normal. When I reinstalled the braziers (some in different unrelated rooms than before), the temperature went back up to 29C.