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This can be caused by a blockage in the exhaust system. Not sure if you have the original exhaust on it or not but if you do it has a catalytic converter on it. They can become plugged up causing the issue. You can remove one of the front oxygen sensors to verify if it runs better when hot than you know its a blockage in the exhaust. If the exhaust is clear than I suspect what you have going on here is a issue with the fuel system. Fuel pressure should be 30-40psi while running. When the problem occurs you connect a fuel pressure tester to the system if it is not within that spec I would highly suspect a fuel pump. They are known for cutting out when hotter. The test port is located on the fuel rail I have included a photo.