Cute little game. Firstly, I would make it a bit clearer that there are multiple fireplaces you have to turn on; it took me a second to realise I wasn't trying to maintain that fire but was actually turning on several.
I would also strongly recommend you add a minimap of sorts or guiding points to show where all the fireplaces are. I got a bit lost when looking for them.
I liked that you could very clearly see that your fire was running out via the character changing size and that you could turn yourself back on via oil or the fire.