(deleted)
the cover of the unit will have a schematic diagram.
you should start out by getting Fritzrig and making a copy of the original diagram
then label each part, make model, etc
note the rating of each part. amps, volts, etc
keep that schematic as your factory unit
then copy and save as your Arduino version
then determine if you can use an original part, or of you need to make a new part, or if you have to replace with some part that is rated for the same output, but can be controlled by an Arduino signal
the project does not seem to be a beginner project, but with your training in the device, the work will be easier for you than for someone who does not know how the device works.
there was a long thread recently about something with a heat pump. that might be a good place to start on the controls/Arduino side