Radiator Fans Only Run When AC Is On

2006 Base model Town and Country.

It started getting a bit hot in slow traffic. I can run the heater inside and keep the engine temp down, but that ain't going to work in Atlanta summers.

I checked when it was hot and the fans aren't running. If I switch on the AC, the fans run. But running the AC in slow traffic doesn't keep the temp down.

I'm thinking that relay in front of the radiator, but if that was bad, would the fans run at all?

I'm thinking coolant temp sensor, but I believe I would be having other symptoms with the engine performance.

Bueller? Anyone?

Thanks.