how to handle internal concrete walls?

I have three internal separation 10" concrete walls. Should I insulate them first or just put frame against them?

Are there any signs of moisture on these walls (efflorescence or staining)? Tape a sheet foil or plastic at least 10 x10" in size against the wall 2-3' from the floor for a week (maybe even in a few places, especially a foot or so from an intersection with an exterior wall), and see if the concrete under the sheet looks damp or in any way different from the fully exposed wall.

Apparently none of the areas is independently heated or cooled, so why would insulation be a factor?

Lessee...

...subsoil temps less than 50F... (check!)

....design frost-depth of 48"... (check!)

...concrete partition intersects exterior foundation wall with no exterior insulation... (check!)

Nope, no insulation needed here!

Compared to Cave Creek AZ with ~70F deep subsoil temp, and a 100-year design frost depth of 3" that NEEDs no frost-heave considerations on how deep the foundation footings need to be...