Lincoln Continental Temperature Swings

I have a 1989 Continental, 3.8ltr with 110,000 mi. Recently, the temperature has been swingiing from normal to almost overheating, all within the space of going through 1 or 2 gear shifts. The temp comes up with the revs, and goes back down immediately when you stop or coast. The car will sit and idle all day and stay at the correct temp, but will rise way up inside of 1/4 mi if you drive. Then, back down again within secods if you stop. I'm talking 50-60 degrees of change. I flushed the radiator, changed the thermostat, and replaced the lower hose (I thought maybe it was getting sucked shut by the pump), but it still persists. Any help would be greatly appreciated.