I have a 2003 Jeep Grand Cherokee Overland with automatic climate control. The drivers side blows cold air constantly. It has no heat.

Sounds like the blend door motro may be bad, this motor is screwed to heater box, there are a few of these motors one for pass/side for hot/cold air then one to control position of air like defrost or vent or floor, then the driverside cold/hot air, i think this motor is on driverside part of heater box, to make sure locate each motor while moving all controls until you spot the one that doesnt move, then remove it and move door manualy to see if you get heat, then replace that motor, hope this helps,