My arms are a network of scars from working in the kitchen...most of them clear up within a few months, but I have a few that are years old and still fading.
I use a big heavy rubber pair of oven mitts at work....they're awkward, but I get used to them after a while. If I need more dexterity, we also have cotton/polyester knit gloves, like the ones you wear in winter, only with a looser weave. Three or four pairs of those with food handler's gloves on top and I am good to lift rotisserie chickens straight out of the oven and slide them into their bags.
For burns, we keep a vial of vitamin e softgels. snip one open and smear it on. for serious burns it takes actual burn cream, but the vitamin e will clear minor burns (and sunburn) up easily.