Hello, welcome and thanks for asking your question. My name is*****'m a Certified Auto Technician with 29+ years experience. I will do my best to assist you. please keep in mind that I may need to ask questions of you before I can answer. When you reply please feel free to add as much detailed information as possible pertaining to your concern.
From the description of your concern, it leads me to believe you are having a problem with the Recirculation Door Actuator. The intermittent cold air and the clicking is the clue to the Recirc Actuator. The problem is the Actuator itself, the gears have internally stripped which causes the clicking noise. Replace the Recirculate Door actuator and all should be well.
To replace the actuator, remove the glove box assembly and you will be able to easily access the recirc door actuator for replacement....
Keep me posted and let me know if you have any additional questions...
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