^^^^ this is correct. Deep Litter is a SLOW compost method, MUCH cooler than hot composting yard waste. It produces measurable heat, yes, but not significant heat - in much the same way that (for most purposes) 1/16th inch is measurable but insignificant. The key to deep litter, apart from ground contact, is to fill entirely with "brown". "Green" like fresh grass clippings will create a traditional hot compost system, and add extra moisture to the coop - which is unwanted.Oh, this page:
https://www.fresheggsdaily.blog/2012/02/deep-litter-methodcoop-cleaning.html
I don't think that litter is doing what the poster thinks it is doing.
That material is all dry, and it crumbles and breaks apart into dust, which collects at the lowest level.
But it is not actively composting and giving off heat.
Of course the floor is "warmer" in winter just because it is better insulated, but insulation does not make heat. It just keeps the heat wherever it is (so not a problem in summer either.)
If you want it to actively compost (bacterial action), you need to add water to it. Don't do that indoors
I think what you were originally planning should be fine, although I might begin with only 2-3 inches rather than 6. You can keep adding bedding, and let it build up, and eventually clean the whole deep pile out once a year or so.
If you get concerned about temperature, stick a thermometer down in the bedding and see what temperature it is, or stick you hand in it to see if it feels hot.
If it DOES get too hot, you can clean it all out and try something else. But I'm pretty sure it will be fine.
One nice thing about chicken bedding: you are not stuck with it forever. If it doesn't work well, just clean it all out into the compost pile and try something else. Or start dumping something else on top of it.
In general, I prefer materials that are in small pieces and can be scratched around by chickens (wood shavings, wood chips, dead leaves, short pieces of hay or straw, etc.) I do not like things that are in long pieces (this often includes hay or straw), because they make a big tangled mat that the chickens have trouble scratching and I have trouble cleaning. I typically prefer a mix of materials, based on what is available free or cheaply at each season.
and here's my deep litter (and deep bedding)