When I looked into new tires, I heard of opposite suggestions in that the heat build-up may expand or warp Kevlar beads more than wire beads. The trade-off is that a wire bead could heat up and aid in melting the tube. I had found arguments on both sides, and ended up buying wire-bead tires even though it killed me to buy that old fashioned technology. (I haven't bought wire bead tires for 15 years until these.)
Anyway, I haven't had problems down the steep switch-back roads here, but I pace myself. I love speed and hate having to maintain lower speed descents because of the rim brakes, so I'll probably shop for disk brakes one day.