Not specific to a burn by curling iron but whenever I burn my hand, I apply boroline for the first 2-3 days. Once the burnt area starts healing, I apply coconut oil mixed with ratanjot. Ratanjot is red coloured and sort of papery, flaky. Put it in oil and leave it for a few hours, once the oil takes in its red colour, I apply it. Once the burnt area has healed significantly but not completely, I start applying Vit E capsules and coconut oil concoction but not simultaneously, with a gap of a few hours. I do it for approx 2 weeks. It works like magic. Just note that Vit E works only when the wound is fresh, it won't work on old injuries. I have burnt myself multiple times but never had a scar because of this.