CHECK te CTS ohms, if you are truly getting hot temps, then your cts should read low ohms, normally if you have a bad CTS your ecu will overcompensate your fuel and retard your timing due to the ''hot'' engine temps even if its a cold start and you get low ohms it will still compensate fueling and timing for extreme hot engine temps.
to me your problem almost sounds like a mechanical problem did you check your compression? getting any exhaust smoke? oil in coolant coolant in oil?
the CTS is more of a electric than mechanical in a sense that it read the coolant temps and adjust the fuel and timing accordingly ie: if the coolant is cold it will adjust the fuel for warm up untill the cts gets to a certain degree then it will adjust for that temp ie: like a coolant temp enrichment ie: fuel vs: coolant percentage..then if your car gets really hot and goes out of parameter for the cts then the enine will be sent into limp mode and overcompensate fuel and timing to keep the engine safe.
if you are lierally getting really hot engine starts, then you migh have a legit mechanical problem ie: water pump,thermostat,headgasket ect
jut my .02
^ in short, pull your spark plugs and check to see if they are fouled with carbon on them from the engine running rch from the cts going bad.
then pull the cts sensor clip and start the car it should run like normal if its the cts becuase the car will see a default tempature that should let the car run normally on start up...
if the plugs arent fouled and the nplugging of the cts doesnt help...look elsewere