Like everything in life, it will not be as simple as that.
It will depend on how 'standalone' the climate control unit is, or how much it may rely on inputs from the vehicle. Experience of Fiat is that the body computer will not contain any features not applicable to the modle as built, so if it needs to output anythign to the climate control, that may only be possible if those outputs are also used elsewhere.
The climate control uses an outside temperature sensor, usually fitted inside the left mirror housing. If that feeds directly to the climate unit, fitting and wiring it in may work, but if it needs to feed into the body computer, and then the signal is duplicated for the climate unit, it may not work. The climate may still work without, but may not respond to temp changes as promptly as it should.
Ideally you need a wiring diagram for the model, and trace all connections to see if they are there, or can be created.
Then from a workshop manual, read the description of the climate system, to understand its operation, which will help if it needs external inputs.
I think this is likely to be a real headache. Whilst the climate control is nice in my Panda, if it goes wrong, it is much more complicated and expensive to fix than a simple aircon system. Do the research before taking the car to bits. If you have a problem with the current system, fixing that might be a whole lot easier.