You will need a bucket and a flask of embalming fluid. (creature product from mummies and elder mummies).
You have to use the flask of embalming fluid on the bucket and the bucket will start to glimmer.
There's a 'temple' inside shadowthorn that has water, you then use the bucket on the water and then you can extinguish the fire.
Do not note that this is part of a much larger quest and it's how you tame the Crystal Wolf.