This is a very vehicle specific question. You're going to need to ask again and specify what you're driving. Include make, model, year, and trim level. Causes include software errors and clogged evaporator cores and operator (driver) error and much much more. The fix can be as simple as removing a fuse for a few minutes, or it can be an all-day project.
Generally, though, I think the most common causes are that you're either driving a very very old car or you're driving a GM.
Temp blend door actuator is bad on the passenger side assuming you want both sides to blow cold air.
heater control valve is bad on the drivers side.
Bad "blend door" actuator or stuck blend door on the driver's side.
Most likely the warm-cold air separator got stuck or the servo (or rod if you have manual air system) mechanism failed.
Why does my Lincoln LS V8 Blow cold air on one side and hot air on the other side
Hey kenneth==It is the directional door not operating properly. It may be a problem with the controler. GoodluckJoe
It is possible for hot air to be coming out of the driver's side and cold on the passenger's side if there is a dual temperature control on the heater/AC unit. Try adjusting the temperature controls to see if that fixes the problem.
passenger side temp acuator has gone bad
The flap is stuck open that controls when and where the heat goes
You need to replace the heater coil !
As the coolant ravels from driver side to passenger side of the radiator, it should cool down.
Check the following........... 1. A/C heater control doors. 2. A/C heater controller. 3. Trash in the heater box. 4. Partly clogged up heater core.