If you have a 180 thermostat, the coolant temperature shouldn't get much above 180. If it's a 190, it shouldn't get much above 190.
Either the fan itself is burnt out or the temperature control switch that tells it when to turn on is bad.
Drain plug on bottom of radiator.
The 1997 Oldsmobile Cutlass radiator fan switch can be found in the fuse box. The radiator fan switch will be in the third column, second from the bottom.
Bottom of radiator. If it has none then remove the lower radiator hose to drain the radiator.
The 1996 Oldsmobile Cutlass Supreme temperature sending unit can be found on the front of the engine. The temperature sending unit will be a few inches above the thermostat housing.
The drain plug is no the lower left hand side ( driver side ) of the radiator.
Follow the top radiator hose down to the water outlet on engine. The stat is in there.
Located in a removable housing at the engine end of the upper radiator hose
Look at the engine end of the upper radiator hose in a removable housing
No water in the radiator
The driver's side radiator fan is the main one that cools the radiator. The passenger side fan only comes on when the engine is being taxed (for example when towing). If your air conditioning still works try turning it on and I'll bet that the passenger fan will begin operating ( the ambient temperature has to be above 3 degrees Celsius for the AC to operate).
The coolant temperature sensor is located in the intake manifold. Also, the hi pressure switch in the AC line. Also, the relays in the fuse box on the passenger fender.