In the books, the Headmaster's office can seal itself against powerful wizards who try to intrude, so it would be strange if ordinary fire could get through the door.

I think the door in the dungeons is an ordinary door made of stone. If the Fiendfyre can burn through the door, does that mean it also burns all the walls? That could cause major structual damage to the castle! I can see a few different ways it could work:

• It's like gas pressure and looks for the easiest way to expand – it'll only burn rock until it breaks through into another open space.
• It can't burn the door, but it can push through the cracks around the door until there's enough on the other side.
• It doesn't have the power to burn very much rock, but it's intelligent or semi-intelligent and likes killing people and/or destroying valuable objects, so it attacks the door on purpose in order to get to them.

Also, what can actually stop Fiendfyre from expanding? In the books, they escape by exiting a magical room that's different every time you enter it; what if you cast Fiendfyre outdoors? Here are a few of the many possibilities:

• It would actually burn the whole world, but only a few people have the skill and interest to learn to cast it, and none of those people have ever been stupid/omnicidal enough to try it.
• It would burn the whole world, except that a lot of people know how to put it out by magic, and it doesn't become much harder to stop just because it expands wildly.
• It doesn't actually gain power from expanding or burning things, and only expands until it runs out of the energy given to it by the person who cast it.

I think my favorite interpretation is that it's intelligent and can only expand by consuming magic, which it can get by burning magical objects or killing magical people. On the other hand, it can keep burning for a long time by just sitting in the same place, so if you seal it in, it's only safe until the seal is broken again.

In this particular situation, how they deal with it afterwards isn't important enough to make it onto a page, but it's easy to explain here. Snape knows about Fiendfyre because ze's studied the Dark Arts extensively. Snape is also sensible/cowardly enough (take your pick) that ze doesn't try to go extinguish it zemself, but blocks it, evacuates the students, and alerts the Ministry. At that point, Granger (who knows about Fiendfyre because ze's studied everything extensively) arrives and extinguishes it, possibly with some help from Snape or the other professors. Normally, Dumbledore would be able to do that, but Dumbledore isn't exactly in a position to do so right now.

Also, I decided that there's an old wizarding law that says a person who casts Fiendfyre and lets it run wild must pay a penalty of fifty Galleons to the person who extinguishes it. So, in the present, Granger now knows that Zabini's family owes zem fifty Galleons. Ze hardly plans to collect.