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This is incorrect.
Hot tyres + hot track = lots of grip
Hot tyres + cold track = less grip.
It's not that simple however, as there is the potential to overheat the tyre and thus loose performance.
It is however a common misconception that cars run quicker on cold days, car generally run faster in warmer temperatures.
It's not a misconception, just perhaps misunderstanding - a car's engine performs better in colder air, even more so in humid air - winter fog does wonders for engine response and "get-go".
Of course, nowadays, with electronic gubbinsery, the effect is either more pronounced (performance-fueled engines; restrictive intake) or subdued (economically-fueled engines), not to mention that tyre grip is probably a more significant factor for most cars.
Either everyone missed the pun, or I am the only one who thought it was funny...