Ford heat problem

If you're basing your assumption of heater core flow on what you see with a garden hose hooked up, you will be disappointed. If the motor is coming up to temp, there are very few things that will cause your symptom.... (honest... engine size and the presence/absence of A/C doesn't mean a damned thing).

Plugged heater core would be the main consideration.... head pressure on your garden hose is like 50PSI or better.... the water pump can't compete with this, especially considering all the additional paths for coolant flow. Erosion of the water pump impeller is a possibility though we would "expect" (but not necessarily see) overheating at some point or another.

Once the motor is up to temp, turn the heater on full blast.... if the heater hoses are close to the same temp, flow is good.... if there is a noticeable difference between inlet and outlet hoses, flow is likely restricted.

Did you make sure you got all of the air out of the coolant system?

What does the engine temp gauge read? You may have a failing thermostat.