My temp before installing winch & stinger was ALWAYS 210. Never had issues even in San Antonio. After installing the stinger & winch, while UNDER 50 MPH, I run normal and stays at 210. However, when at highway speed (55-60mph) constant speed, it creeps up and stays up. However, when slower, it drops. So it does effect cooling. This has been seen in multiple TJs that are owned by friends, as well as JKs. And these are with smaller winches installed, for example the Smittybult XRC8. Not a huge wench at all, but big enough to cause issues.
As for the fan clutch, if there is no airflow through the radiator, it'll be running at a higher temp & radiating the heat which engages the fan clutch. So the under hood temps do have an effect. Absolutely no way that the under hood temps CAN'T have a factor because it's heat that engages the clutch to run the fan. Which, in turn, can add load to the engine pushing that fan constantly if the temps don't happen to decrease.
Those are the points that I was trying to make.
JEEP = Just Empty Every Pocket!!!