While I haven't found an official answer to this question yet, I played the game some more and it seems to me that it is more in the spirit of the game to leave the hot spot in place, even after putting the flames out.
Considering that there can only be a limited number of new hot spots (placed via flare-ups) - 6 for all difficulties except Heroic, where it is 12 - it seemed too easy to just get rid of them quickly.
Also, when placing additional hot spots at the beginning of the game, they can be placed on open spaces without fires; therefore it seems to make sense for them to remain even after the fire is extinguished.
Edit: Neal Tibrewala confirmed in the comments that there really is no way of removing them. (Thanks.)