As a cook who has had severe oil burns cold water will only tighten the skin quicker and cause a more painful recovery period. Lukewarm water soaking immediately after the burn is best. Maintaining moisture on the burn area will reduce scaring. I had a burn on my thumb form roux molten hot roux. I left my hand in a vinyl glove for about 2 weeks before allowing it to start drying. It swelled the first couple days with water blistering up, I just drained it and left the dead skin on top til I remove the glove after 2 weeks. I removed the dead skin and allowed the fresh new skin beneath firm up. Never did I itch or have pain moving it during recovery and no visible scar.