It could be one of several things, but my first inclination is to look at the lower radiator hose. If the internal spring is missing or rusted away, the hose can collapse under vacuum pressure, thus creating a restriction. When you slow or stop the hose goes back to normal shape and allows coolant to flow normally.
To check the fan clutch, have the car idling at normal operating temperature and shut the engine off. If the fan clutch is OK, it should stop rotating almost immediately with the engine. If it keeps spinning for several rotations it's bad. Usually with a bad fan clutch you'll find overheating at idle when it should be locking up with engine rpm...just the opposite of what you're experiencing. At speed the fan clutch should be free wheeling anyway.
Other things to check...tightness of belts, seals properly installed around the radiator and air deflector in place under the front end.
Start with the easiest and most basic...belts then work up to more complex. You should be able to squeeze the lower hose and feel whether the spring is present. Visual check of the fan clutch and whether seals are present. It could be as simple as slipping belts.