At the phone company, where I was a mechanic for 30-years, when a driver complained of no heat it was aways one of three problems. The most common problem was a slightly stuck open thermostat. In the winter, the engine won't reach operating temperature if the thermostat is just stuck open a little. The first thing you do is look at the temop gauge to see if it is reaching nornal temperature. Then touch the upper hose to make sure it's hot. The least common problem was the hot water shut off valve to the heater core. Most cars don't have them. They are comptroller by a cable, or a vacuum operate valve. When they fail to open, hot water does not reach the heater core. A fairly common probelike was a plugged heater core. The way to check it is to grab the two hoses, one will be hot, and one will not be. That tells you no coolant is flowing through the heater core is. Determine the direction of flow, the hot hose would be flowing into to core. Remove the hot hose from the heater core and the cold hose from the engine. Take a garden hose and reverse flush the core through the cold hose If you are lucky, you can unplug it. I have seen mud come out of them like tooth paste and then they work fine again. The heater core is not designed for garden hose pressures so start off with the least amount of water you can.
As far as the direction of flow through a heater core. I had very smart neighbor with an engineering degree. I know he was smart because he moved out of CA to Tennessee and left me behind here. He was the head engineer at a million-sf cold storage refrigeration plant. We had this conversation about the direction of flow through a radiator. He said, if you want to cool a radiator core you flow the liquid from top to bottom. If you want to heat the core you flow, it from bottom to top. I have early Mustangs too, so I use a lot of illustrations from them to explain things. These are 1965 Mustang heater hose routing illustrations. The hot water is flowing out of the intake manifold and back into the suction side of the water pump. Notice the hot water hose from the intake manifold flows into the bottom of the heater core. The opposite direction of flow than the radiator.
