Mark, in most cases, it's not safe to say that the poly sheath of the Dbl Braid slings protects them from heat damage.
The sheath does protect the core. But if it is a polyester/polyester double braid, half the strength is in the cover and half is in the core. If you do heat-damage the cover, you may be reducing the strength of the sling by as much as 50%!
If you are using a double-braid with high-modulus core, then most (almost all) of the strength is the core. In this case, heat damage (or any damage) to the cover is not as much to worry about as in the poly/poly dbl braid.
love
nick