The mesh covering the predator has nothing to do with the cloaking, if this was the case every inch of the pred would be coverd in the mesh, which it isnt. Other wise their heads would be coverd in it also, end of pred 2 when the elder cloaks & uncloaks, no mesh on his unmasked face, hand ect is there. In the movies it was just for the look but in the comics & books it gave ref to the meshgiving off heat, keep their temps to a high level.
Predators have a thick outter skin, we see this in both movies, ie when pussy face injects himself.The outter skin is very tough & thick but over time would of course burn to the softer tissue. In avp it was just a short blast of a flame, not full on fire. With the skin and armour which is heavy in avp the flame isnt gonna do much harm really is it.