What type of headgear is shown in this Renaissance portrayal of Hell?
score:2
I think this is almost certainly a biretta. I think this is either a Moiré hat or possibly a chaperon variant. Fra Angelico lived from 1395 to 1455, in Florence. At the time it seems that headgear was fairly fashionable and is well known from paintings.
If you look at his works (many can be found on wikimedia), he has painted a number of different headgear on various persons, including those worn by commoners, so he was certainly familiar with the current styles and painted what he saw around him. It would seem that at the time headgear was transitioning from the common hood into various styles of hat, both brimmed and unbrimmed, but usually round in configuration and without points. A complicated hat known as a Chaperon was also used, but this usually involved having a cape (known as a patte in French and Foggia in Italian) which was tied around the hat and/or under the chin.
I mention these to indicate that none of these look at all like the tri-corn hat shown in the Last Annunciation, and that he painted other hats in greater detail in this work, as seen here:
Source:Fra Angelico, Public domain, via Wikimedia Commons
If you look at the foreground of the main panel (bottom third) you can see the living (as opposed to the dead saints with halos in the top 2/3), the living are being sorted into those going to heaven (left, escorted by angels and shown with what could be described as progenitor halos) and those going to hell (right with demons). In these masses you can see several different styles of hat, including caps, chaperons and religious head-gear (mitre?) and monks' hoods. Now, all these are in the main panel, and as such you should expect them to be painted in greater detail as the artist would generally focus on the main object of the work (i.e. the centre panel, with the assumption taking place), rather than on the side panels. However, notably none of these hats look at all like the ones in the side panel part being asked about by you.
Caps: 
Chaperons: 
Mitres: 
Hood: 
So - we know that Fra Angelico was well aware of the hats and the styles worn by various people, and that he knew the significance of what people wore which styles of hat. In addition, we can see that he has religious people being sent to hell (he was a priest after all, and even beatified in the 1980's). So, the hats in question could well be biretta on priests, put there as an edification for the viewer to show that even the "good" could fall to the wiles of evil. From a comment by @DamionKeeling, the characters wearing the hats have long hair, this likely indicates they are not priests after all, but rather either scholars or gentlemen.
I have found an excellent resource called "The Mode in Hats and Headdresses" by R. Turner Wilcox, which as illustrations of many of the styles found throughout history of the Western and Middle Eastern world. This is only publicly available through the following link on Archive.org as far as I can tell, but is easily viewable if you have an account.
Notably on pages 50--52, there are illustrations of hats from the 1300s through to the 1500s. Of particular note are two illustrations, which I have screen-shot and provide below, with the captions associated with each.
From this, I lean towards a Moiré hat, but the voluminous chaperon is also a distinct possibility.
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