Sierra4000,
To my knowledge, there aren't any rubber chemists that hang out on the internet - I don't know why.
I am not a rubber chemist, but I have worked along side some very talented ones and have picked up a few things over the years. Keep that in mind while I try to answer your question.
When it comes to tread rubber compound, there are 2 things going on. Friction and mechanical grip. Racing tire tread compounds take advantage of both. By being naturally more sticky, and by being softer so the rubber penetrates the macro texture of the pavement. It's this penetrating the macro texture that makes the tire NOT behave according to normal friction theory (grip proportional to the load). That penetration increases the point at which the maximum occurs, but also changes things such that the tire has to get a 10% to 15% slip to generate the max grip level.
So it isn't just softness that increases the grip - and measuring the hardness of the tread doesn't necessarily measure the relative grip level between dissimilar tires.
Temperature? Yes, temperature has an affect on grip and I suspect that both friction and mechanical grip are affected in different ways - and it will be different for different tread compounds.
