It's the coolant temp sensor that you're thinking of. There is also a fast idle thermo valve that stops bypassing air after the engine warms up.

Your problem isn't either of those though, it's the fact that with the larger throttle body you're getting more air into the engine than the throttle position sensor and the MAP sensor are measuring. You've not got more air with the same throttle position basically, which is making the car buck while driving.

Because the throttle plate is closed at idle, your idle problem probably lies with TPS adjustment. If you've swapped your TPS over to the other throttle body, and haven't calibrated it, it's probably off. When you unplug it, the ECU looks up a default failsafe value and uses that, which works OK until you actually drive and the TPS reading would be different than that. The TPS doesn't care if the engine is hot or cold, it just reads what the throttle position is. The IACV takes care of hot idle throttle bypass, and the IACV and FITV both take care of cold idle bypass. The idle regulation is different based on the coolant temp sensor reading though, yes.

So check the TPS adjustment, and set that if need be. Also, you should always reset the ECU when you do any type of modification like this, because the ECU will be confused if it's learned/stored values are different than the new values that are being read from the sensors.

Is the FITV on the throttle body on your car, and did it swap over to the new throttle body?