Heater core (radiator) needs to be cleaned or changed
Hard water, and calcium can build up insite the hoses and get released in chungs during the flush process. These pieces can get caught in the thermostat and cause it to fail. You can try removing the thermostat or just replace it as it is an in-expensive part. You might consider re-flushing the radiator as more calcium might hit the thermostat after replacing it.
The thermostat on a 2001 Cadillac SLS is located in the radiator. To access it, remove the upper hose assembly after draining the radiator halfway.
The 1999 Cadillac thermostat can be found on the front of the engine. The thermostat will be inside of the thermostat housing. You can follow the top radiator hose directly to the thermostat housing.
By the thermostat
Low coolant? Radiator probably needs flushing and/or replacing after 40 years. Bad thermostat? System airbound? Water pump not circulating coolant? Hoses collapsing? Bad radiator cap?
Engine end of the upper radiator hose
Make sure the radiator is full of water, don't just check the overflow tank, but do make sure the car is cold before removing the radiator cap. Also the thermostat could be frozen closed or you could have a failed water pump. Try replacing the thermostat and flushing the cooling system first. Don't forget to buy a thermostat gasket when purchasing the thermostat.
Usually in housing at engine end of top radiator hose
Drain the radiator. disconnect the top radiator hose from the engine. Remove the water inlet that the hose was hooked to. The thermostat is in the housing. Replace the gasket when replacing the thermostat.
Usually at engine end of upper radiator hose in housing
Probably at the engine end of the upper radiator hose
near the thermostat housing