1988 Oldsmobile 98 Brougham 3.8 litre

A bad radiator would explain the problems but other problems could be a bad thermostat (if it's stuck closed the hot coolant won't return to the radiator to cool down), they're only around $10 if you run out of other ideas. You can also check to see if your water pump is bad, there's a bleed hole that will drip out coolant if an internal seal has broken. If you want to check your water pump, start up your engine and look underneath your engine compartment for any dripping coolant.

If you're so inclined you can check out your radiator also by draining the radiator from the petcock, and then removing the two large hoses, remove the radiator cap, and then flush water into it with a garden hose from the top inlet. If your radiators in decent condition water will come out the bottom at the same rate it's being poured into, if it's coming back out the top then you might have a plugged up radiator.