Why would a 97 Wrangler be hard to start when hot and run extremely rough when under heavy throttle?

First change the fuel filter. Check the cat convertor.

Is the temp gauge showing the engine running hot? Could be a water pump prob if so.

second the first answer probably a clog in your exhaust,if not my camaro did something similar it was mass airflow sensor,but if that was the case it would register with computer.