Too many variables to be able to give a simple yes or no answer really Dan. It depends a lot on the particular tyre and individual suspension characteristics of the car in question. But tyres always grip better when they are'nt stone cold, as for spinning them up for so long the tread blocks start to melt and go greasy then thats too much! Testing and monitoring tyre temps vs laptimes is the only way to accurately guage the most beneficial tyre temp for your car.
Don't forget the importance of tyre pressuer as a variable too, under inflated tyres temd to deform and move around more which generates more heat in the carcass of the tyre, too much though and steering response and outright grip will suffer, but you can get away with lower pressures on tyres with stiff sidewalls (R888s etc.)

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R H Davey Welding Supplies. I sell new and used welding equipment in the Hampshire area. I take on welding jobs in the evenings, ally casting repairs are one of my specialities but I can weld pretty much anything. PM me with your requirements.

Some of my services: (See my for sale threads)
Engine mount/chassis repair
Solid Beam Mounts BACK IN PRODUCTION
Harness bars