Next time it conks out on you, look down the carburetor while opening the throttle sharply to see if the accelerator pump squirts out gas. If it does not, then you know that you have a fuel delivery problem for sure.
If it does squirt fuel, then you may have a coil problem which only shows up when the underhood temps are elevated. Check for spark the next time it conks out.
When I have a fuel delivery issue, I go about it in a systematic manner.
1) Disconnect the fuel line at the at the inlet side of the fuel pump, looking for good fuel flow. Something might be sitting on the end of the pipe inside the tank.
2) If good flow after step 1 above, I do a fuel pump delivery test by removing the fuel line at the carburetor and attach a hose on the end of the hard line, then put the other end of the hose in a 24 ounce Diet Coke bottle (no exceptions unless you are from South Carolina and refer to yourself as a chipmunk, then a Pepsi bottle is acceptable). Then crank the engine with the starter with the ignition off.