Is a small closet, 3 x 2 x 8 a good enough size for a server, a router, and 2 external hard drives?

Or will it get too hot in there?

I would worry more about the ventillation than size. I wouldn't operate gear that I really care about in a room that gets above 80*. Data centers like to keep their gear at around 68*.

As mentioned air flow is the main concern.

In my room which is way larger then that with a ceiling fan I run 3 PCs, some switches, firewall a router and the temp skyrockets with the door closed. During the cold times it'll shoot up 10 degrees in an hour. During the summer I have to blow cold air from the hallway in here cause it will exceed 95 degrees and stuff starts crashing on me.

Right now it should be fine if its cold in the closet. I would run a thermometer and find out the average temperature. But try not to get it above 75F