I'm not certain, but I was under the impression that Ford had fixed it for the '99 model year, but maybe not. Your problem is exactly what happens when the "blend door" goes south.
There is a cold air entry and a hot air entry to the plenum; the big plastic box under the dash with the heater outlets, defroster outlets and dash vent outlets. The blend door is a flap that controls the mix of hot and cold to give you the desired temperature. It's controlled by a DC rotary servo, but the stem on the door itself breaks, and the servo moves but the door doesn't.
My '97 stuck in full hot when it broke. About a $125 fix if you do it yourself. Since the redesigned blend door won't fit the old plenum, Ford will sell you an entire new plenum with the redesignes blend door in it. You have to pull the whole dash to replace it.
Edit.... here's a link to a possible cheap fix: