As long as it's a quality flex fan, that won't be the coolong problem(except that it will eventually grenade and send shrapnel through the hood!). As mentioned, you can run all day long on the freeway without a fan at all because there is enough ram air coming through the grille. Assuming the radiator is not plugged, I suspect it's either a collapsing lower hose or a water flow problem caused by a mismatch of pulley diameter and/or number of impellers on the pump. I've seen many of these when an engine is converted from A/C to non-A/C or an engine that's been pieced together from misc parts from a variety of sources. Won't be the cap either.....it doesn't control the temperature....it just helps keep the coolant from boiling. (putting the system under pressure, raises the boiling point). Another possibility is too much antifreeze. Pure antifreeze isn't a very good coolant so make sure you have a good 50% mix with distilled water.
Mark