Re: Why does friction increse when warming the tyres of a racing car?

There are several kinds of friction in tires.  The two most common are 
rolling resistance and ground friction.  I'll assume you are concerned with 
ground friction for this answer.

Normal tires become more flexible as they warm.  This means that there is 
more of the tire tread contacting the ground and higher friction.

In drag racing, the tires have a high percentage of polyisoprene in the 
formulation.  When the drag racers drag out prior to a race, much of the 
polyisoprene reverts and becomes tacky.  This tackiness also increases the 
friction between the tire and ground.  The trade off is that drag racing 
tires have a very short lifetime.

Hope this helps.