years. When I was 16 I accidentally touched the back of my hand to a heating element above the fry warmer at a fast food restaurant I worked at. melted right through the skin and scarred. No longer there (10 years later)
When my son was 3 months old, I was holding him while also trying to get something out of the toaster oven. I accidentally touched his leg to the hot door handle and it left a burn about 3 inches just above his ankle. 6 months later and it's pretty much healed and fading.
Young kids often heal quickly and over the years any scarring should fade. But doing the others tips on this post is a good idea.