This is an interesting question that was brought up and looked at by personnel at Black Diamond. They encountered the issue of whether or not a hot belay could melt the slings when you are climbing. Through extensive research, they conducted a study to solve this very question.
Without going into heavy detail about their process and findings, they concluded that because they could not mimic a realistic scenario in which a device would reach the temperature to melt a sling, it should not be a concern.
However, Black Diamond did come up with a list of remedies for those who still worry about this issue. They recommend that when you are rappelling, you do so at a slower rate, rappel with slower loads, anchor with two slings and use nylon slings to anchor with.