Prius c 2014 A/C problem

Looks like a door that controls the flow of the air might be stuck, try by disconnecting the 12v battery for a few minutes and connecting it back on, then turn on the A/C and on max cold, see if it gets fixed, something similar happened to mine but doing this fixed it.

 

This post may give you any clues on how to proceed. It has to be some kind of bad motor/actuator/door that controls airflow. Heat is always produced of course there is typically a damper that shuts off the flow from the hot section when you select max cold. It is interesting that heat is flowing on only one side if I understand what you wrote correctly. I see one other post with the same problem but no solution, but most cars I've seen without a dual zone system (i.e., both driver and passenger have HVAC controls) will control the temp before the ducts split off to the vents on each side.

 

Since I don't have a service manual, just looking at the parts diagrams is leaving me clueless how you could get different temps from each side. Here are the ducts which would attach to it.
https://parts.olathetoyota.com/v-2014-toyota-prius-c--three--1-5l-l4-electric-gas/body--ducts
Here are the blower parts
https://parts.olathetoyota.com/v-2014-toyota-prius-c--three--1-5l-l4-electric-gas/hvac--blower-motor-and-fan
It appears that servo (#5) should control which vents but maybe it is the temp servo. I'd try to listen carefully for the servos moving while you select different vents and temperatures. I'm not sure if you'd be able to see anything moving up under the dash.

It sounds like #5 is major pain to change, but some people have had luck doing a power reset for stuck servos. See this thread. Good luck!

 

#5 on the second link would be the fresh air door servo, apportioning outside air vs. recirculated.

https://parts.olathetoyota.com/v-2014-toyota-prius-c--three--1-5l-l4-electric-gas/hvac--evaporator-and-heater-components shows the other two servos as #12 and #13.

I believe #12 controls the target selection (defrost/face/floor) while #13 modulates the blend door to mix chilled air with heated air to hit the temp target.