i don't know what kind of honda you have so the answers are gonna be kind of generic.there are two fans out by your radiator, one is controlled by the temperature of the motor and one is controlled by the A/C....sorta.in reality, both fans will run when the AC is on, of if the control systems decide it needs to run both to cool the motor.the thermostat is a mechanical device in the water stream, there is no diagnostic system that tests it electrically.if the gauge on your dash is going crazy you probably have an overheat problem that your fans are trying to control.i doubt this issue will cause a O2 sensor failure the first time, but running it hot several times can cause the O2 sensor to heat up beyond its design threshold, and that might cause it to fail.