OK, so work has been just a hair slow lately...
Anyway, I came up with a spreadsheet that lets you look at the effect of running the motor inside the interstitial space, along with a comparison to a full-foam spa. You can also turn the motor on and off, so you can see the effect either way.
It's not real straightforward. Since there's heat going to and from the water, and to and from the cabinet, along with the heat (or not) from the motor, it's just a hair on the awkward side. But it does work....
It also lets you simulate the effect of a forced air ventilation fan in the cabinet, at variable cfm - one suspects that certain spas (the Name That Cannot Be Mentioned
) use something similar.
If you are fairly geeky and into heat transfer, R-values, and BTUs, I'd be glad to send you a copy for your comments. You'll need probably Excel 2000 or later.
Let me know.