My far-from-expert opinion would be that it wouldn't make a difference in smallbore, wouldn't know about fullbore.
Thinking about it, I know that the lightweight FWB barrel is only lighter than the heavyweight FWB barrel because of a difference in diameter of the barrel, and I don't believe that there is any noticable difference in performance. I don't think that there's a difference in performance of an 07 barrel against a 13, so probably any difference caused by heat dissipation is negligible.
But I'm just rambling. I'm sure someone will be along shortly to correct me.