Agree with all the rest of Steve's post. Only,
digitS' :
Composting litter really cannot generate much heat. An efficient compost pile should be at least 3 1/2 feet deep according to
Texas A&M and, hey, that's Texas, not subzero Montana.
The advantage plenty of litter gives can be its insulation value. Expecting the litter to generate much heat from composting has to be something of a stretch. Unless, I suppose, that the decomposing litter is several
feet thick.
But remember they're talking about what you need to get the pile to 160 F. It doesn't take that much heat to warm a cold coop.
I used to clean horse stalls semi-professionally
and there was this one place in NJ that wanted us to pick out the manure but not the wet spots, and just add a little more shavings as needed to keep the top looking nice. Every now and then you had to dig out the bedding wholesale and start again. The bedding would be 1.5-2' deep at this point. Whoa nellie that was hard on the nose hairs, and had to be done when horses were turned out and no boarders or clients were around
But you know what, 1.5-2' of horse pee soaked shavings gives off CONSIDERABLE heat. To the point of steaming quite vigorously and it would be somewhat more than pleasantly warm if you were curious and put your hand down there.
The whole point after all of old-timey deep litter is for it to be DEEP, as in like "keep going til the cows' ears are scraping the ceiling" deep. I have never seen a controlled study of temperatures in coop sized (or barn sized either, for that matter) structures where some had true old-timey deep litter and others didn't... but based on my experiences with digging out those stalls at that one barn, I very seriously believe that meaningful heat would be provided.
Also meaningful ammonia and water vapor when the litter was disturbed, of course
So while it likely *can* provide some heat in some circumstances, I am not sure it is something you really want to count on.
But the latent heat of the earth helps too, as Steve says. My chickens are in a big slab-floored building (which is not too different from an earthen floor, from a heat budget perspective) and it holds its temperature real nicely thru the winter.
You just wouldn't want to do it in an area with less than excellent drainage.
Pat