Flushing heater core steps

[mpierce9]

Hello, 1975 K5 Blazer 350 with A/C. I'd like to flush the heater core.

Here's why (skip down to The question if you don't care and just want to read the question)
It's cold outside. Heater never blows warm air. I checked the cold/hot door attached to the cable on the dash panel, this is working as expected. Put on a new thermostat earlier this week, the temp gauge reads med to med-high after driving for about 10 minutes. There are two hoses attached to the heater core housing. One hose is attached directly to the radiator, the second hose is attached to the water pump. The hose attached to the water pump going into the heater core gets very hot. The hose attached to the heater core going to the radiator does not get hot at all. Seems like there is something blocking the water pump hose from the radiator hose somewhere inside the heater core.

The question:
Is this as simple as unhooking the inbound and outbound line and plugging a water hose up to and just holding down the trigger until it runs clean and clear?