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On my Jules verne device, I have 3 sensors:

1. Coolant Temp Sensor AKA the "CTS" (two prong, responsible for mixture)

2. Thermo-time switch (two prong, switches cold start valve on when cold, for certain amount of time)

3. AND THE MYSTERY "Temperature Switch" 61 31 1 357 753.

...I can't seem to remember or locate any info on this.
Can somebody tell me what #3 is for exactly?

Is this an emissions item?
It plugs into the ignition harness on my car and I know isn't present on the 528i.

for the cluster reading ?

Thanks for guessing-

But No, the guage for my cluster is on my thermostat housing.
Its not that.

Anybody else?

I am going to take a guess too since I am not sure. My 76 530i does not have it since I have a 3.3 from a 1980 733.
The hint you gave that it connects to the ignition harness tells me that the switch signals the ignition to prevent the spark advance when the car is cold for, as you guessed, emission reasons.

Hmmm. Maybe its for an auxilary air fan?

My fan actually has a toggle switch prior owner put in next to the switch that was put in for the cb radio. Lol

This switch alone controls my aux air fan, im thinking maybe prior owner bypassed the system? Can anybody confirm?

I can tell you that's not it.
The cooling fan is controlled by a sensor switch on the radiator, bottom left. Some cars have 2 sensors (low and high speed) and some cars have a combo sensor with 3 wires, controlling the 2 speeds of the fan.

Ah ha!

You were right. Its a little ambiguous in the manual, but when looking at the parts diagram in tandem it is apparent this 45 deg cel switch is responsible for keeping the EGR valve shut until the coolant warms up.

Since I am desmogged, I am glad I dont need it.

Cool.