CHAZ,
I would think you should sight it to the fixed barrel, then adjust the other one to the same POI. If the adjustable barrel moves inside the "hanger", you should be correct about the heat transfer. BTW, I helped a friend "regulate" one of the Russian O/U 30-06s, that adjusted by different diameter spacers between the barrels. I had a "Bear" of a time, I couldn't get it to be consistent for anything. Then I noticed the heavy scope he had mounted was moving in the mount and the mount was moving on the barrel. I had him send me another ( lighter)scope and remounted it tightly with Loc-Tite(blue). When I finished that time, it was back with the original spacer( I had made 5 others). The moral of the the story is to show; if you use a scope, be sure it is a light one, solidly mounted.
Mike