If you want a simple way to turn it off and back on every hour, maybe one of these will work? (at least for 20 hours)..
Timex Electronic 7 Day Timer for Use Inside or Outside The House | eBay
You can set up to 20 off-on cycles for each day.
I'm using one of these to keep my A7 AirTap off during the late night hours.
So far, it's working just fine.
You might want to use one setting to keep the ASHP off between midnight and 4AMish..
Since it's not likely to be needed during those hours..
I like these timers so much (and the price), I just ordered # 4..