Heater valve controls

Thoughts and suggestions please!!!

You might find this hard to believe but we have no idea what size motor you need for a honda civic. Your question is meaningless without a photo and maybe even the datasheet for the motor that is factory installed (if there is one). If you have no idea then we at least need to know the specifications for the motor in terms of torque or load and the accuracy required. You cannot possibly expect us to know that information for a Honda civic. You have to do YOUR homework before you post here. Get all the required information and then post a photo of the cable you need to drive back and forth. Take measurements of the cable travel.
Take measurements of the available space where a motor would go. Look online for motors. Look for Servo drivers for the motors.
The motors used for most arduino project are simple dc motors or steppers. We rarely get projects involving a servo motor capable of precision positioning (PID control). That is not to say that it is not possible, just not that common. Try spending some time
with Google. Coming here and asking for "Thoughts and suggestions " is fine but I hope you are not expecting us to design a servo controlled system for you, because that is probably not going to happen. Gather the information we need to give you suggestions first, and then after you post that , we'll give you our thoughts.