Well, I think I found the problem with the Escort's heating system.
Yesterday evening, I took took the thermostat housing out of the escort, since all the diagnostic indications I could find pointed to a faulty thermostat. Just for background, the way the cooling system in a water-cooled car engine (all of them, except pre-1980 volkswagens and Corvairs): There's a water pump (probably a centrifugal impeller) that draws water from the radiator and pressurizes the water jacket inside the engine block that surrounds the cylinders, usually at the bottom of the block. On the other side of the block, near the top, there's an outlet that goes to the upper radiator hose that carries water to the radiator, so the coolant (water/antifreeze mix) flows in a closed loop. At the outlet point on the block, there's a mechanical thermostat valve that opens when the cooling water is up to temperature. This is a remarkably stable technology; it's been done the same way for tens of years, at least. The engine computers have temperature sensors for for air and coolant, but the cooling system is actuated by this purely mechanical valve.
Here's what one looks like; this is the one that I took out of the engine:
The ring forms the seal between the water jacket in the engine block and the outlet hose. The spring at the bottom sits in the water in the block, and when it hits the proper temperature, it pulls the core of the thermostat down, opening the way for water to flow up.
I think the problem with my car was the rubber seal was distorted and didn't seat right, letting some water get past it no matter what its temperature was. It's possible that's because they installed the wrong thermostat, which was slightly too big and had to be jammed into the thermostat housing. Here are the two thermostats, the one of the left is the one I removed, the one on the right I bought at the store the other day
The outer diameter of the old (nonworking) one is slightly bigger. The new one on the right slides into the thermostat housing pretty tightly. On the lower right corner of the left thermostat, you can see where the rubber seal is distorted.
Here's the thermostat housing, looking from the point of view of the engine block if it was installed
and here with the new thermostat installed
It's supposed to get warm here this afternoon; I'll probably take half a vacation day and put this all back together, and hopefully things are better.