1994 Honda Civic Trouble starting when warmed up

I bought this car two weeks ago. The owner said it needed a fuel pump. I decided to start with the fuel filter first and the car started right up. What I found out now is that the car starts up normally when the engine is cold, but when it begins to warm up, it will start to shutter, lack power, and stall when the gas pedal is depressed. When I try to restart it, the car will just turn over and sometimes backfire through the exhaust. If I let it cool down, it will start as though there is nothing wrong again until it begins to warm up again.