Tire pressure goes up from heating the tire (usually about 1 PSI per 10 deg F rise in temperature), which will be determined by the load on the tire and operating conditions like you mentioned above (ie, race track is going to heat up tires much more than normal street riding). Biased ply vs radial may end up at a different max temperature if used under the same exact conditions based on how they flex and heat up with use, but I doubt it's going to be huge difference.
I have checked my radial tire pressure after long periods of street riding in warm weather, and they are usually up 3~4 PSI from a cold pressure starting point of 36~40 PSI, so seems the tires I had at the time were close to the 10% pressure increase from heat.
I usually run my sport bikes tires 3~4 PSI below the recommended settings anyway when riding solo; the bikes I have just seem to handle and ride a little better with slightly lower tire pressure. If I plan on having a passenger, I'll bump the tire pressure up a bit, but take it back down if riding solo later.
