If you get hot air out of the top vents even when the heater control is on it's coolest setting, then your heater control valve is shot. OEM units are hard to find. Not sure if IPD still sells them (pricey). The normal routine is to upgrade to the later style valve. FCP Groton sells the kit. Not an easy fix, takes a couple of hours, but does the trick.

If your fan is staying on, you have a switch or relay problem. If your '90 still has the rheostat, then the microswitch on the side of the temp control is bad. Sometimes they can be adjusted to get more life out of them. You'll see it on the side of the thermostat when you remove it from the dash. If, as I suspect (I can never remember) your '90 has the blue switch for AC, then your switch or AC relay is bad and sticking closed.

The fan running and your vents blowing hot air are not really related.

DS