Some designs of Trombe Walls have air gaps. The narrower these gaps the better depending on many variables. From these variables, wall design, air temperature, solar radiation and solar radiation incident angle.
Trombe wall does not have an air gap. Trombe is a thick wall (sometimes 1 m thick) that transfers the gained heat deep into the ground as a means of protecting the room(s) behind it. Double walls with an air gap within is a whole different story. The air gap acts as a barrier that delays heat transfer through the wall, resulting into a time-lag or time-shift, that slows down heat transfer till night when the outer temp is lower than the inner one. This makes heat turn around and flow to the outside again.
So basically, both systems have the same goal; protecting the inner room(s) from external heat. However, the way to achieve that goal is different in the two cases. I believe mixing the two strategies would mess things up and you end up achieving less performance than the original two.
Some designs of Trombe Walls have air gaps. The narrower these gaps the better depending on many variables. From these variables, wall design, air temperature, solar radiation and solar radiation incident angle.
Please refer to the following paper, it may fulfill your inquiry.
((54- Faris S S, Chaichan M T, Sachit M F and Jaleel J M, Simulation and numerical investigation of effect air gap thickness on Trombe wall system, International Journal of Application or Innovation in Engineering & Management (IJAIEM), vol. 3, No. 11, pp: 159-168, 2014.))