What makes burns quickly better?

Keep cooling thesite. Until the tissue is hot the burns continue to damage skin so keep cooling the site immediately after injury. Once the burning stops then apply local antibiotics - neosporin to heal the skin.
Type of burn? What type of burn. If you have a significant burn please obtain medical evaluation and care. For minor burns, apply cool compresses. Applying aloe vera can help with pain and can speed burn healing by stimulating growth of new skin.