Instead of ice, you can try running cool tap water over the burn for about 10 minutes. This helps to reduce the temperature of the skin and ease the pain. You can also use a cool, wet compress to help soothe the skin.
Ice Pack Burn Skin at Kathleen States blog
Now, I know what you're thinking, "But, what about ice packs or cold compresses?" Well, those are actually a bit different. They can be helpful in reducing swelling and easing pain, but you should never put them directly on the burn. Instead, wrap them in a cloth or towel to protect your skin.