But air exposure was happening most of the time, the way I cooled my burns, so it definitely was the cooling, that did help in my case.
(A wet towel with ice in it)
And I learned to not mess with the wounds at all. I think the last time I had a burn, I opened the the blister to get the fluid pressure out. Bad idea, this time I left it and it healed way faster. It healed so good, that after my first night of pain and cooling, I did not had to do anything with it, except giving it a rest.