1999 Cadillac Deville over heating

The water pump is the last thing to suspect. Chances are there's an air pocket under the thermostat that needs to be burped out. Thermostats don't open in response to hot air, just hot liquid. Look for a bleeder screw or plug near the thermostat housing. If there isn't anything, look for a sensor that can be unscrewed, then refill the coolant.

The next thing to consider is a leaking cylinder head gasket. That will put combustion gases into the cooling system under higher pressure than normal, and the air can cause a thermostat to fail to open. Your mechanic can do a chemical test at the reservoir. That involves drawing air from the cooling system through a glass cylinder with two chambers partially-filled with a special dark blue liquid. If combustion gases are present that liquid will turn bright yellow.