Should engine run cooler when AC is engaged?

toolmanmike said
If you have a thermostaticlly controlled clutch fan it may engage shortly after the a/c is turned on

RustyRatRod said
The hotter the temperature gets, the more resistance the bimetal spring gives the clutch making the fan spin harder and pull more air through the radiator

I think the mystery is solved, thermostat fan is doing its job.