I use Pirelli Supercorsa's ... DOT version (mandatory by the racing rules) ... homologated for road use. This is a racing compound, similar to the Pirelli Rosso Corsa for cars.
With road tires, sure you need a couple of km to remove the dirty part, the thiny outter layer (what they used in the past was parafine, today is different product) ... but not more than 100 km. Road tires are less sensitive to heat cycles to my opinion. With race compound, you can accept between 5 and 10 heat cycles, but no more (I mean, a real heat cycle). With a road tire, much more before feeling any degradation.
The only concern I have is with Michelin, car or bike, road or race compounds tires ... I hate these compounds because they really need to have a good temperature, and heated so much to give the max. potential.
Did you check the pressure ?