I've not done this, but my immediate impression/guess would be that the temperature control loop (using Arduino) would be very simple, but the power electrics - mechanical build - and thermal efficiency would be the hard part and wouldn't necessarily be made any easier with Arduino control.
It might even make more sense to leave the Arduino out of the thermostat control loop altogether so you don't have to convert between the microcontroller voltages and 130w switching. Unless you have more complex behaviour in mind than "it's too warm, turn on the coolers!"?