If your contact lenses don't pop out from your eyes, the lenses would not be melted by the smokes of the barbeque. But long time of expose to the smokes will cause eye dry effect, some eye drops can ease your problem.
I never heard that the heat from barbeque can melt the contact lens. However, you should keep away from the smoke because the particles can get into your eyes and stick to the contact lenses and then it will cause irritation.
I've ever heard someone's contact lenses were melt while having a barbeque because he was too close to the grill for a long time. So to avoid the same tragegy, you'd better keep your contact lenses away from the grill or reduce the time that they are exposed to the grill for.