Q: Car runs rough with AC on

It sounds like you may have a bad AC compressor or potentially a faulty MAP Sensor. When the AC compressor is beginning to fail, this may incur an increased load on the motor as it works harder than usual to turn a bad compressor. This increased load causes the motor to work harder than it otherwise normally would, resulting in the motor overheating.

The Manifold Absolute Pressure (MAP) sensor senses engine load and generates a signal that is proportional to the amount of vacuum in the intake manifold. The engine computer then uses this information to adjust ignition timing and fuel enrichment. When the engine is working hard, intake vacuum drops as the throttle opens wide. The engine takes in more air, which requires more fuel to keep the air/fuel ratio in balance. When the computer reads a heavy load signal from the MAP sensor, it adjusts the fuel mixture to slightly more rich than normal so the engine can produce more power. The computer will then retard (back off) ignition timing slightly to prevent detonation that can damage the engine and decrease performance. This may also be caused by other closely related components such as a dirty or failing mass air-flow sensor, a faulty throttle position sensor or potentially a vacuum leak. I would recommend having an expert from YourMechanic come to your location to diagnose and inspect your vehicle.