I have the opposite problem on a '97. Hot air blows out in the driver footwell, even when the A/C is on.
I presume that one side of the heater control valve has failed. The heater control valve is under the hood near the brake master cylinder.
I want to be sure that this is the problem before spending $225 on a heater control valve because I have to pull the air plenum off the firewall to get to the hoses on the heater valve. I replaced the heater hoses on my other '97 and it is a PITA. If I have to do this heater valve, I will obviously replace ALL my heater hoses while I am in there.
When I get time, I will take a voltmeter and try to figure out how the heater control signals the heater control valve. Then I can create a signal, or cross the wires, to see if the problem is the valve or the heater control.