A few different things come to mind, but it would be helpful if you had more info... the first thing I thought of depends on whether or not the tank has been off the bike recently... on my `zook, I have to be *very* careful how the fuel lines from the tank to the carbs are routed when I put the tank back down, or what happens is the engine heat makes the hoses "soft" and they will crimp themselves closed after a short time and starve the motor for fuel... took me a while to diagnose it because it was intermittent and only happened when the bike got good and warmed up. The other thing I was thinking is that electrical components (especially ignition coils) tend to not work as well when they get hot... could be just old spark plugs in combination with a marginal ignition and when it heats up there isn't enough juice in the system to make the spark. Is that bike fuel-injected? If so, then I'd also wonder about engine temp sensors and perhaps the FI "brain"... but that's out of my range of personal experience, just a guess. If it were my bike, I'd double-check all the fuel-lines under the tank, and replace the spark plugs (perhaps even the high-tension leads as well) and then see if anything improves.
...ummm... assuming, of course, that what you mean is that the starter turns the otor over just fine, but it simply won't fire. If the starter won't turn the motor, or does so, but only slowly, then I'd start looking at the battery leads, battery itself, and perhaps the solenoid switch and connections for the starter motor.