I have a 96 lincoln towncar. It has an digital heating/air condition control.?

Temperature blend door is stuck. By opening the glove box, looking toward the left in the back you can see the blend door motor, with the temp. set as cold as you can put it, tap on the box with an extension, then it should move to cold.

The reason for your towncar blowing hot air only is no doubt because one or more of the tempeature blend doors inside of the heater aren't working properly. Normally there are vaccumm diaphram motors that control these doors. More often than not these motors have small rubber hoses attached to them and these hoses become brittle and crack over time. The hoses leak vaccumm there by not operating the temp. blend doors there by not letting any other setting of the heater to operate properly. The air conditioning part of the heater could be having the same problem as the heater part. Or maybe you are low on Freon in your air conditioning compresser. But I would check into your vaccumm hoses first. Cause if these are leaking vaccumm you won't be getting proper operation of any part oy your heater or air conditioning system. The smallest crack in a vaccumm hose can cause the biggest problems.

the blend door motor connection has broken they don't work on vacuum anymore its electric and Lincoln Towncars have a poor design where the blend door connection to the motor breaks usually you can hear the motor running trying to operate the blend door listen for that. Its very time consuming to replace which means if you take it to the dealer its expensive to get repaired.

Could be a couple problems One the AC is not charged and it will blow warm air when not charged ..second its got a blend door module that is computer controlled that switched from heat to cold that could be bad. This module is controlled by the computer.

Try checking the hot water valve, that goes to your heater core. It could be leaking hot water passed when its shut.