From personal experience, it's luck and all random. I remember once no Thornfire Wolf appeared for me when the whole fire was cleared. The next time I did spawn a wolf within 30 minutes from what I can remember and that was the time I got the mount. However, I didn't stick around for anymore. If there's any stats I can find I will try my best but I've looked around a lot of websites and can't find a solid pattern or percentage. I'm curious as to others experiences as well.
I've watched videos and someone had mentioned that he spawned 1 within 30 minutes as well and the other 4 within an hour.
There is a small chance that some Thornfire Wolves will spawn when you try to put out the fires, but not every fire will spawn them. Regardless of where the fire is being put out, the Wolf will spawn west of the lake, here.
When Thornfire Wolves are spawn, a red message will be broadcast : Unleash the fire wolves and burn the house of the enemy.
EDIT: Also, because of this question the next time I'm able to I'll test this out to post recent stats on the summoning of them as it's been a year plus since I've summoned them myself.