[cotbu]

In correct it wouldn't matter if it was hot or cold for the tps to be the culprit.
Coolant temp sensor, has multiple errors that are visual and audible, he is not acknowledging any of them. So using deductive reasoning, its logical to say it's the tps. If the ecu has learned the value maybe not so much when warmed up.

some of the cts problems would be, rich idle, rpm fluxing, and hard to start warm or cold, and maybe a code or two.

The symptoms are not exact in anyway, we could have asked a multitude of questions to narrow down the solution, but this is zilvia! you tell us the problems we don't tell you...! OK sometimes, but whatever!

Not saying its not cts, just i wouldn't start there 1st in this situation.