This will happen if the temperature blend door actuator position pot is dirty or not working at all. The controller hunts to find a "happy place" but cannot so it keeps on cycling. I would try and replace the actuator, 9 times out of ten the problem is the motor portion of the system.
Here is a guide to help you see what you are in for when doing the job.
https://www.2carpros.com/articles/replace-blend-door-motor
Here is where the temperature blend door actuator is located in your car (below)
Align the air temperature actuator with the door shaft and rotate into position.
Install the air temperature actuator screws to the HVAC module.
NOTE: Refer to Fastener Notice.
Tighten the screws to 1 N.m (9 lb in) .
Connect the electrical connector to the air temperature actuator.
Calibrate the mode actuators by simultaneously pushing the A/C and RECIRC buttons on the HVAC control module 3 times each, within 2 seconds of initial push.
The A/C and RECIRC button LED's will flash while this calibration is taking place.
The calibration will take anywhere between 10 to 30 seconds depending on battery voltage.
The LEDs will quit flashing when the calibration is complete.
IMPORTANT: Any time a mode actuator or the HVAC control module is replaced, the HVAC control module must be calibrated to ensure proper air distribution.
Cycle the ignition and verify proper operation.
Install the instrument panel compartment.
Check this image below. Temperature, Defroster, floor and panel in that order
Let us know what happens and please upload pictures or videos of the problem.
Cheers, Ken
Images (Click to make bigger)
Sunday, November 19th, 2017 AT 1:30 PM