will the cooling fan work if I disconnected the cylinder temp. Sensor

The Fault:

Temp Gauge went suddenly to the maximum, Engine light came on, engine vibration increased and doesn't run smoothly

Note: Actual engine temperature is not high

Trouble shooting:

I disconnected the Cylinder Temperature sensor, the temperature gauge doesn't move but engines runs normally and smooth

My Question Now:

Will the cooling fan work & the cooling system work properly if i disconnected the cylinder temperature sensor till i replace it ?