How to respond to an upset student? My finals were held recently. Due to some timetabling issues, I had to organize for some students to take the finals early, but still within finals week. The dates were mutually agreed. 

One of these early final takers was very upset when I stopped them writing at the 2 hours and ten minutes mark after starting (for a 2 hour exam).  After they gave me their paper, they looked very upset and stomped out of the room.

They performed poorly on the exam but eked out a D overall for the class.

The fastest student in the class finished in about 45 minutes; the majority were done by 90 minutes. I don't usually set time-critical midterms or finals.

When the student was upset, I didn't respond at the time nor did I follow-up with them afterwards via email or in person.

Should I have done anything more? If so, what?

I believe that college should be about more than just grades, and wanted to give the feedback to this student that their behavior was extremely unprofessional.
I would not intervene unless I felt the student was at risk of harming themselves or others.

As you say, college is about more than grades, learning how to handle failure is part of life. 

Moreover it’s not unlikely that their performance on the final was the icing on the cake: they had a bad day/week and were upset about all of it plus the final.

Unless you’re willing to allow them to retake the exam (which is probably a bad idea unless they offer a good reason), reaching out to them and telling them they should deal better with exams will likely annoy them and demotivate them further.