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That is *only the thermostat.... the thermostat controls the much larger refrigerator sized system with a fan and compressors in it. It is something like the steering wheel in a car. If the car doesn't run it is not a steering wheel issue, but an issue with the motor.
The determination of the unit that this thermostat controls being the correct size or not, and adequate ducting or not, or if it has enough refrigerant in it or not. etc etc..
If you can send me pictures of *that unit, both the big part inside the home, about the size of a dishwasher, and the unit that sits outside the house, about the same size, I can be a lot more specific.
Use the paper clip icon at the right end of your tool bar above, or the 'attach files' link to the left of your 'send' button to attach the pictures.
We can go from there.