Way back in the LFS early days we had a discussion about tires, temperatures, thread depth and tire longevity.
As far as I can remember the conclusion was that (and it makes sense in my mind) is that as the rubber carcass thins out, the heat contained in it gets less. Or rather, the amount of energy it can store. So that way the surface temperature gets more important than the carcass temperature. So basically your tire cools off alot faster and heats up alot faster. So that means your surface temps spend far less time in the sweet spot, and THAT is what give you decreased grip, in addition to the obvious chemical degradation of the rubber itself. You enter a corner with cooler tires than before, and exit with hotter tires than before.