Any kind of sport oriented rubber is just fine for the average trackday participant... you'll be fine on the the diablo corsas, they're designed for EXACTLY what you have in mind for them. I've heard NO support for them overheating on the track under the use of an average trackday rider. Your first few trackdays are nothing more than a spirited street ride... if you wouldn't ride them hard on the street, don't ride em on the track, simple as that.
"Warms up quick" does NOT equal "overheats and gets greasy".... Unless you're in the fast group & rarely getting passed i'll be very suprised if you get it too hot.
Tires I've used on the track w/ my '00 zx6r:
Metzler M1's - great street tire, good trackday tire... got a little slippery on the track towards the end of the day, but i was movin pretty good
Pilot Powers - loved em, great street/trackday tire.
Pirelli Diablo Supercosas - a true DOT race tire. Good luck getting that greasy.
I run the Supercorsas on my EX, but it's also a RACE bike, not a street/trackday bike. Which means i'm riding as agressive as I possibly can. If i were only doing trackdays I'd get a set of Pilot Powers, Diablo Corsas, Metzler M3's, Dunlop Qualifiers or something along those lines.
If you find yourself able to overheat the Diablo's (dont think you will), then worry about your next set of tires.