Look at the heater hose leaving the intake manifold near the rear of the engine routing toward the firewall. A short distance from the engine there is a tee. Disconnect the 3 hoses from the tee and take the tee out for inspection. The leg of the tee toward the engine and the leg toward the firewall (the heater core feed) should be unrestricted. The third leg of the tee that goes toward the front of the engine should have a small restrictor in it. If not, buy the correct tee from a Cadillac dealer and install it. That tee is not a generic part but it is often replaced with a generic plastic tee without the restriction and as a result the heat does not work.
While the hoses are disconnected hook a garden hose to the engine hose leading toward the firewall (heater core feed) and flush the heater core. You will see the water coming out of the hose that leads toward the front of the engine. Alternate flushing the heater core in the opposite direction using the hose leading toward the front of the engine.
All you need to do is disconnect the three hoses at the tee to check the tee and flush the heater core at the same time.
After flushing you should refill the system with coolant and check the concentration of the system in the radiator to make sure it is 50/50.