Had this exact problem myself last week. The fan clutch is probably getting sloppy on your car, as it was on mine. Get the car up to operating temp sometime and then shut it off and pop the hood. Give the fan a spin by hand. If it spins pretty freely, then yeah, your fan clutch is shot. I replaced mine with a "heavy duty" fan clutch and all is well again.
DO NOT get the "severe duty" fan clutch, though, unless you want your car to sound like a giant Hoover vacuum cleaner; those things are like having the fan permanently engaged rather than the fan clutch allowing the fan to "slip" a bit above a certain RPM, so it makes it noisy as hell and will affect your horsepower and even your gas mileage (I lost about 2 MPG while I was running one).

You can tell it apart from the standard OEM-replacement fan clutch visually and by feel. It's way thicker than the stock fan clutch, and it's reeeeeally stiff when trying to turn it by hand. Oddly enough, it was also $7 CHEAPER than the OEM replacement fan clutch for some reason.
Having a trimmed fan shroud and/or a few nicks out of the fan blades may or may not make a difference, but it won't be enough to make it overheat. (Not having a shroud AT ALL might do that, though.) Probably wouldn't a bad idea to replace the fan at the same time while you've got it off to replace the fan clutch. Old plastic fans tend to crack around the center hub, and you don't want that coming apart at high RPM and sending pieces of plastic into your radiator and everywhere else.
