Gina,
The contact with the leaves may damage some of the leaves, but only if temps are sufficiently hot, which is likely the case since you are trying to create more heat. That said, if you damage a few leaves, so what? You are close to fall and losing the leaves anyway, so some defoliation is not a really big hit at this time, and might even have the "perverse" affect of allowing more sunlight onto the figs, giving you more of the additional warmth you are seeking.