If TW sensor connector permanently disconnected, it will trigger CEL but not if partially locked or intermittent.
By the way, No CEL (or no warning lights) doesn't mean you don't have error code stored.
Some failure modes require two consecutive detection or even two drive cycles before triggering the CEL. For example, some of the O2 sensor related codes.
I always have CEL code
#36 stored on ECU as I disabled TCS by disconnecting the TCS controller.
It won’t trigger CEL because for code
#36 , it needs to be detected twice per cycle but since there is no TCS controller connected, it can only be detected once per IGSW reset.
Hence, code stored but no CEL.
I don't know if it's possible to mix up and install TW (black connector) and rad fan sensor (brown) by mistake (diameter, thread) or even connect the mating connector properly (extra key on the connector).
Even if it was possible, your rad fan would be spinning fast even when the engine is still cold so very unlikely to be the case.
Hope you used the OEM sensors.
Since it's thermistor, you can just measure the resistance at the ECU connector once eng fully warmed up.
No need starting the engine or even the IGSW.
This will tell whether the ECU is getting correct temperature info or not.
Check paint lock on the idle air adjust screw of the TH body.
It's grey from the factory so not easy to distinguish.
This will tell whether someone touched it or not.
Doesn't mean it was re-adjusted wrongly but at least, removes the headache of cleaning all that hardened lock paint inside the small screw hole before new screw installation.
You will have hard time doing it while preventing the piece of paint dropping inside without removing the TH body....
Kaz