How does framing a very tall non-structural wall differ from framing a standard height non-structural wall?
Structurally I think you have a bigger problem with the two story space than with the taller one story space. 

If you put a lot of weight up in the air 10’ or so without anchoring it to something or providing some shear bracing, it could tip over by lateral loads or racking. If you put gypsum board on the walls that will help, but may not be sufficient depending on the upstairs load (weight).

I’d plan on about 20 psf to 30 psf horizontal force on the walls, depending on where you live, because if you open an exterior door during a wind storm that force will transfer to your new walls. The same force will be applied to the 20’ high walls, but it won’t have the weight of the second floor furnishings, people, etc. acting as a high center of gravity. 

Even without the wind, you’ll have a tendency for the second floor to rack. 

Gypsum board has some horizontal resistance when nailed properly. However, even when it’s nailed properly, it’s horizontal resistance is not close to plywood. If you use the plywood shear approach rather than the 2x4 wall brace approach, be sure to use adequate anchor bolts into the concrete slab floor. 

I know you don’t want to install 2x4 braces over to the exterior structural walls because of possible heat transfer, but that is a minor issue compared to the horizontal structural issues.