If you're thermostat was bad or not working right you would likley be experiencing overheating issues with you're car.
The statement about how a cooling system and fans on a car works is becuase of the above statement that you made.
If that were the case I would have just took my thermostat out to acheve lower temps instead of buying a 160.
These fans on our cars do pull a lot of air and while I guess it is POSSIBLE that if the fans COULD keep up it may be able to keep it from overheating theres 2 things that would NOT happen.
It would not be a steady tempeture.
It would not be anywhere near 160*
The stock PCM fan on/off settings are-
Fan 1
212*F on
207*F off
Fan 2
226*F on
223*F off
The problem is more than likley in the climate control system. Such as one of the blending doors being stuck on the upper vent setting only.