How to calculate whether it's worth turning on a fan to bring warmer air to a heat pump hot water heater?

I have 4 new Rheem 50 gal heat pump hot water heaters being installed in the basement of my home/multiunit property that is a 4-unit building (one heater per apartment).

Generally speaking, the attic is warmer than the basement. It occurs to me that it might make sense to move some hot air from the attic to the basement in order to make the water heaters more efficient. I could put a temp sensor in the attic and a temp sensor in the basement and only turn on the fan when there is a certain delta between them. Sounds like a fun arduino project right?!

My question is – how do I determine when it’s worth turning on the fan in a more robust way? For example, I should probably consider how much energy the fan consumes and compare that to the energy saved by providing warmer air to to heaters. This is where things get out of my pay grade. The air would likely be exhausted near the heaters, or I could investigated ducting directly to the intake.

For the sake of getting some numbers, let’s start with the following:

• 4" duct at 30′
• A 30 watt inline fan
• The Rheem heater I’m using is the XE50T10H45U0 model
• 3.75 Unified Energy Factor
• I live in Maine
• Other factors?

Thanks for playing along!