1994 Town Car outside temperature shows -39 on the dash gauge. Air conditioner will not blow cool air but the heater works fine. How can this be fixed, or can it?

YES! The Ambient Temperature Sensor is tied directly to your EATC unit. (I just perused the schematics) Yes it can effect your AC (since the lowest temp setting is 60.) There is also a Sun Load sensor (in the dash) As stated by my associate, it is likely that you have an open in either the sensor or the wiring that is causing your -39 degree reading. It is also possible that you have a freon leak preventing the AC from operating but it doesn't sound like it - yet. Ok, to fix it - you're going to need access to the trouble codes for the EATC system - perhaps a good service manual. It's probably a sensor failure. I am uncertain if it is a Federal Law or just good practice but most electrically/electronically operated automotive HVAC systems default to heat/defrost. So you won't freeze and you can see if all else fails. I know that the dealer is an unpopular choice but...rather that than throw parts at it until you get lucky - or not. A reputable luxury car mechanic is another choice if you aren't inclined to tackle the job your self.