I read somewhere that the cooling fans have two (may be more) speeds. Is that thue?

If there are speeds, then is it working by the computer using pulse-width modulation (PWM) or is it only two speeds due to some wiring trick in the fan's DC motor armature winding?

If it's the latter case, then there should be two relays (one for each speed) and there is a chance that only one is malfunctioning causing the closed loop temperature control system to get messed up and bounce.

I drove, yesterday, for several hours after bringing to coolant back to around 60% and purging the system well. Using the OBDII scanner and a wireless microphone I attached to the fan to see when the work. I noticed the following:
1. It takes a relatively long time of serious city driving to bring the temp to around 210 (about 30 mins).
2. The thermostat opens at around 197 and closes at around 191.
3. Most importantly, the fans work high speed when AC or heat is on, but not without. They only work high speed at around 219 which is kind of too much unless there is a low speed operation that was supposed to start at a much lower temp in the range of 200-210.

Anyone with a 2004-2008 who knows about fan speeds?