Your fan is coming on too much, too soon. The fan will spin even when things are cool because of the fan clutch, but it's slipping until the temp rises enough to lock the clutch up. When the fan clutch locks up, the fan will spin at the same rpm as the clutch hub. You'll definitely know when that happens because it sounds like a jet engine just went to full thrust under your hood. On some summertime trips from VA to FL on I-95, my fan clutch locked for a couple minutes about 3 or 4 times during an entire one-way trip. Outside temps were at 100+ deg during these trips. The fan didn't come on & off repeatedly like you reported. If the clutch doesn't function as it should (locks too much or not at all), you should replace it.