Is this a new problem, or have you always had this problem?

Besides the useful posts above, you might check out your fuel tank pressure system. Tank lid o-rings can get worn and the lid open during a run.....leans things out. Crack in tubing near the pipe or tank nipple.

Worn out engine...often they die shortly after they start...once everything warms up, all compression is lost.

Tuning.....biggest culprit of them all....the notorious too rich LSN and too lean HSN can easily cause your problem. You think you are OK as the engine accelerates well.....but it is running on excess fuel built up in the crankcase due to a rich LSN. Eventually that gets used up and you wind up running based on the HSN which is too lean and the engine gets hot.

Some people are a little picky about thier temps....just how hot is it? Anything between 220 and 290F can be typical. Try to tune for best performance....rich enough the engine doesn't sound like it wants to blow-up (high rpm screaming) and an obvious smoke trail at WOT. Check temps then. I don't worry too much, but definately like to see the temp below 300F as the engine leans out due to runnning out of fuel.