I'm no expert--I had no idea about the bedding getting too hot--but hopefully my response will BUMP your
thread and get someone more knowledgeable to post

.
I've been doing deep litter for 2 years in my duck house. I live in the pacific northwest, so it really doesn't get too hot here, and my duck house is well-ventilated and shaded and so I've never noticed it getting too warm in there. The ducks often go there for shade. I've never noticed the bedding steaming or getting too hot. It dries out, but that's about it (I have ducks, which are wetter than
chickens as they splash and have more liquid poops. The bedding is usually moist under the top layer even during the summer). I'm
thinking, but I really don't know, that if your bedding was getting to hot/steamy, you could cool it down by adding some more bedding. But, I really don't know. Hopefully someone else does!
As for how I use it, I haven't put much effort into it. I just steal some from the duck house whenever I need to mulch around fruit
trees, or build up
garden bed. I do have some in an old recycling bin that I'm composting/aging, mostly so that I don't have to worry about salmonella/listeria when I top dress herbivorous food plants with it. I'd like to compost all of it so I can use it on more herbivorous plants, especially as mulch, but I haven't had the time to set up a system. So, I just use it as mulch around fruit trees or on my blackberries/raspberries during the winter (the cane fruits LOVE the bedding), or use it to create/build up beds. I've also used it successfully as mulch over covercrop seeds such as buckwheat and daikon radishes that I do not plan on eating. I throw down the seeds, scoop some bedding from the house, sprinkle bedding on top of the seeds, and then
water. The plants sprout and grow fine, and I didn't have to poke the seeds into the soil or till the soil, etc. I have to assume that, even if it's not composted completely, the
carbon in the pine shavings balances the nitrogen in the duck poop pretty well. The only plants that
did not like bedding straight from the duck house were my blueberries and huckleberries--they don't like much nitrogen and got nitrogen burnt by the application of non-composted bedding.
I'm thinking that the logs in your
chicken coop/run won't stink too much. My ducks poop on the bricks in their house. It gets a tad stinky, but there's air flow and it mostly just sort of dries out. Every so often, I pry the poop off with my pitchfork and add it to the bedding. As long as the poop moves around and there's good ventilation, I wouldn't think it would go anaerobic on you. And, since you're keeping
chickens and not ducks, the chickens will supposedly scratch and turn the bedding, so the poop probably won't stay on the logs long
enough to stink as the chickens will scratch it off. I only have one chicken, and have yet to notice her doing much of the bedding turning, as she prefers to roam about my property, so I really can't definitively say that they will keep the poop moving for you. But, even if they don't, you can always come by once a week with a pitchfork or other tool and scrape most of it off and turn it into the bedding.
Hopefully someone with more
experience and/or knowledge in composting (and chickens!) will come by and comment, as many of your questions go into the science of composting that I really haven't taken the time to grasp fully. I added your thread to the composting forum in hopes of someone there spotting it.