where is the temp sensor lacated

This could also be from a blocked heater core, or from the inside sensor not sensing the air temp being warm enough to release the hot air into the cabin. Many Cadillacs had this feature so you didn't get cold air blowing on you right away. The coolant temp sensor will be located in the engine block. There may be a shutoff sensor in the lines to the heater core as well.

Water pump might be seizing up. Expensive job (about $600-700)