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A properly working heater core should be able to run you out of the cab.
Suggest to -
* ensure the temperature blending door / damper is closing fully. This can be inspected by removing the access panel located behind the glovebox (take the glovebox out, about 8 screws, and voila). You should see the heater core straightaway, the damper kinda has to have the line-of-sight just right.
* ensure the coolant level is full. What you describe is a typical symptom of low coolant, BUT low coolant isn't the only thing that could be causing the problem.
* make sure the thermostat is working properly and is the OEM-rated temperature. I always seem to get the thermostats that go bad by not opening, leaving me stranded - but there are those that fail by not closing, and those that just don't have a thermostat at all.
1989 F150 XLT standard-cab shortbed 4x4, 5.0L, AOD, 3.55 gears, manual hubs, 31x10.50 tires, 218K miles. Repainted Oct09. SOLD - Jan2015
2014 F150 XLT standard-cab shortbed 4x4, 5.0L, 6-speed auto, 3.55 gears, auto hubs, locking diff, trailer pkg, 5K miles.