Experience with thermal glues/adhesives?
Almost any adhesive will be suitable. Thermal adhesives are better, but that's missing the point.  Some numbers from wikipedia:
Air has a thermal conductivity of 0.025  (W.m-1.K-1).
Aluminium is about 200, so that's a ratio of 10,000 times.
If you can fill the gap with thermal grease (0.9), or a polymer like epoxy (0.3), or even water (0.5), the thermal resistance of the gap will decrease by about 100 times.

3M claims a thermal conductive epoxy with 0.72, but this is not much better than average plastic around 0.3 to 0.5. The important thing is that these are all 100 times more conductive than air, and they fill the gap eliminating the air.

So select an epoxy that meets your mechanical needs, something with the right temperature range and flexibility. You can probably use it somewhat above it's high temperature limit, as you don't need full strength. Prepare the surfaces properly and fill the air gap.