Behavior sounds normal to me Quantifying "heat up" with actual temperature gage readings would help.

The viscous fan clutch keys off the radiator exit air temperature. On my car it typically tightens at about 100C coolant temperature. At idle speed it does not produce much air flow, but once up to 2000 RPM audible "fan roar" is noticeable.

If the idle period is long the coolant will continue to heat up, and the electric fans engage high speed at about 105C. The electric fans rapidly bring the coolant temperature back down to about 100, and it will continue to cycle this way at idle.

Once I get the car moving at steady speed over about 35 MPH the temp will drop below 100C.

Duke