Engine misfire after warms up

This vehicle only has 43,000 miles on it. It starts and runs fine until the water temperature gauge reaches 180 degrees. Then the engine starts to run rough. It idles okay but from 3,000 to 4,000 rpm it starts to misfire, backfire, pre-detonate, and the water temperature quickly jumps to 210-215 degrees. Both of the cooling fans operate but only on high.
Neither the "Service Engine" nor "Service Vehicle" lights illuminate so there are no codes. I checked for them anyway but there are not any codes so at this point I am just guessing.
I took it to a Chevrolet dealer to have it troubleshooted. They claim that the problem was a clogged catalytic converter. I replaced the converter and both oxygen sensors.
It did not correct the problem. Since it seems to be a timing issue I have changed the spark plugs, spark plug wires and the three coil packs. Also, since the car had not been driven, I have drained the gas tank and replaced the fuel filter.
I am still having the same problem.
I assume the computer is getting bad information from one or more of the engine sensors but without any codes, I do not have any idea which one to start with.