My AC blows hot air out the driver's side and cold

There are a number of things that could be going on. Do you get cold air out of the passenger side vents? Have you tried sending the air to the defrost vents, or the floor? Do you get cold air out of those when you do?

There should be ( 2 ) slide switches or buttons that control passenger/driver side climate control, one of the switches is not operating correctly and probably be faulty. I have a 1991 Buick Regal with the same problem, sometimes i can slide the faulty one real fast to the right and back to the left and it will work fine.

its probably the actuator. its usually located under the dash in the center. you might be able to get to it by removing the glove box and looking to the drivers side. its a black box that has a wire connector on it. switch your heater control from hot to cold and you should here it click. replace it and i bet your problem is solved

It sounds like your passenger air mix actuator is broken. I believe many LeSabre's have seperate driver/passenger air control.
Here is a useful link I found: http://www.buickforums.com/forums/showthread.php?t=17002

This problem is likely due to a failed part called the blend door, this door has an electric motor drive, to replace it requires the dash be removed form the car entirely. The blend door is a door that moves back and forth between the AC core and the Heater core to provide cold hot or a blend of air flows from both cores to give the desired temperature. Other issues can cause this and due to the cost or repair a through diagnostic should be done to confirm my guess is correct about the door being the problem.

To troubleshoot this types of problem,click the link below :----http://howtobyme.blogspot.in/2012/02/heater-blows-only-from-defrost.html
--------Go through the procedure to confirm the issue.

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Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

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Heat blows cold on drivers side and hot on passenger side?

http://schematicsdiagram.blogspot.com/2011/12/heat-blows-cold-on-drivers-side-and-hot.html

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This will help.Thanks.

may have a bad blend door actuator.

you have a bad left temp door actuator. its on the lower left side of the heater box held on by 2 or 3 5.5 mm screws. It will most likely need calibrated after replacement

• Assumed your AC unit is OK, but uneven temperature distribution. Try to throw the heater on an off severtime. A sticky valve on the heater would cause similar problem.
  
• Observe the RPM while parking your car. While the AC cut in cut out (or turn on an off). If it cause no load on the engine. The freon may be low or the compressor is bad. In this case only the intake side of the evaporator is cooler than the other side.
  

broken cable? if possible trace the cables back to the box move then bolth and see if one doesnt, if so you could alwase manually move it for a temp fix