Well here are at least a couple of ideas. One possible problem could be vapor lock. The engine compartment could become warm enough the gas is on the edge of going from liquid to a vapor state. This is not that uncommon, my fuel injected ski boat will experience the same symptoms when under heavy load on a hot day. To solve that I run the blower on hot days, problem gone. Additionally it would not hurt to inspect the fuel system and replace filters. I would even go as far as dis-assembling the carb to inspect and clean it. Those steps are probably not needed but at least you will know the condition of the supply side.
Back to the possible vapor lock issue, does the engine have enough fresh air intake to keep a good supply of fresh air avaliable? I suspect if you let the engine rest/cool for a few minutes the problem is gone. Checking the coolant system to ensure proper cooling is also in order, as that would increase the temp in the engine bay.
Good luck I suspect the solution is an easy one.