Hi Chris,
I have just ordered an Arduino kit with another project in mind, but when I saw your post I thought, "That looks useful!". We have a Mitsubishi heat pump system too and so I would be very interested in any info you would be prepared to share, it's a great system but lacks a good programmable controller.
I have not used Arduino before so this kit (when it eventually arrives) will be my first experience of the platform, so I don't have too much idea about the power consumption of the board and wireless set up, but could you use a rechargeable battery set with a discrete solar panel somewhere nearby? Just a thought.
Paul