I'd have to go with heater core. A little FYI: if the 88 Taurus is like the 87 Taurus I had several years ago...brace yourself... It is VERY expensive to have it replaced. I think it was a little over 8 hours of labor.
Best guess the valve that opens the line to let water flow is either stuck or it could be a vacuum line problem some did have cables u would have to check to see what u have u can also google ur issue lots of blogs for car issues
I have a 2007 with the same problem. It was diagnosed with an actuator not being able to be tripped with a possibly warped vent door that switches between hot and cold. It#039;s not cheap, either. I was quoted $1062 in labor alone. Only thing was, the car came this way and Lithia won#039;t fix or accept responsibility for it, despite the warranty, that#039;s now dead. Good luck for your car.