The main thing you need to make sure of is having enough air in the tyre to prevent it peeling off while cornering, spinning or coming off the track. It does happen. As for the pressures you want to use, only testing will find that out. I run 38-40psi hot in my tyres all round, but I turn up with 38psi cold to avoid any chances of peeling in the first session and drop it down once I get back in the pits. I do lose a bit of front end grip as the tyres warm up. I did try 36psi hot once and the sidewall flexed too much and the wear on the sidewall is showing me not to try it again. But things will be slightly different for different cars. I probably should point out that all this is on street tyres.

If your running semis/slicks, just ring up the company and ask them what their thoughts are.

If you are new to the track days, running too much tyre pressure could be a help since it will slow you down a bit and give you some extra time to think.