I am writing a work of fiction in which, circa 2030, the global average temperature of the Earth falls by 150C (~270F) over the course of five months. This upends the way societies work as people desperately try to survive.
Due to the speed of the cooling, people will forego rationality and science even more than in the current real world. They will try all sorts of things for heat even though they know they are living on borrowed time.
One of the things that came to my mind is settings forests on fire to heat a small town. Chopping down the trees for fuel would have been smarter, but the clock is ticking and axes are not always available. So somewhere in the world, some group of people is bound to do it.
My question is, how effective would a forest fire be in heating up a catastrofically cooling small town, and if it turns out this is effective, how long could it last?
This question is not about the side effects of the fire, such as ash and soot making it hard to breath. I am already expecting things like these to happen already.
Edit for clarification: people would not wait until the Earth is a solid ice ball to try that stunt. I am imagining people doing that by the time it starts snowing around the equator, which should be much before even a month and a half into the cooling.