Maybe. If you think about it, the plugs, plug wires, etc are in use while the engine is cold. Everything is managed by the ECU, using preset values. After the engine warms up, the ECU relies on inputs from the sensors. The CTS tells the ECU when the engine it is warm. In theory, the idle is then controlled by ECU using input provided by the IAC. Something is either providing incorrect input, or the ECU is interpreting the input incorrectly.