Plenty of people have reported this happening to them when a bushfire or a firestorm occurs, as with you. I think it happens a lot if you manage to get lava to surface levels.
Having been near a real one, I have two comments to make: Firstly, I would have loved to have had a pause button or an automatic pause so that I could have dealt with the psychological situation of a great big destructive force, let alone done something about preventing the damn thing. Secondly, they are definitely world changing events in my opinion. So yeah, I can see why they cause the game to repeatedly pause.
The quickfix that everyone recommends is to turn off the cave in pause and zoom functions until the fire dies back, as laularukyrumo recommended. Some people just turn off all the pause and zoom spam, but that can be a problem if you have something else critical going on (for example, lava pumping, or even the unexpected, like Mooding).
There is another prevention method: make sure that there isn't a great deal of tree cover for the dragons to burn up in future: Total clearfelling. It will not make you amazingly popular with the elves, but if you've not got easy access to lava, it might do wonderful things for your glass/pottery/metal industries.
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Interestingly, underground fires don't seem to do this. I've had a few fiery forgotten beasts (are they becoming more common?) down there in the Deeps, and they have set fire to the underground mushroom trees, and everything else on the level, and the water the trees were burning over turned to steam, the beasts the trees were burning over burst into flames themselves, but there was no constant "something has collapsed!" spam. Has anyone else noticed this, or am I on my own?