Cooling Fans 97Jetta GT HELP!!!

Seems like my cooling fans are finicky. They'll come on if the car is in park and has been running for a few minutes. I'll take it out for a spin and after approximately 30mins of driving, shifting gears becomes a little eratic...shifting from 1 to 2nd takes a higher RPM and so on with 3 to 4th but while engine is cool, shifting is normal. Fans do come on when A/C is turned on. Also notice after long durations of driving and I turn off the engine, fans are not running. Temperature gauge on my dash is right at center so it doesn't seem to be overhaeating. Replaced the Engine Coolant Temp. Sensor, flushed out the old coolant and added new G11 but still the problem persists. BTW, its an automatic.

coolant fan control module under coolant resivour is common failure.