Which vintage of 4B? They've been using that basic model number for at quite a few years with significant differences between the various incarnations. Do you know when it was made? Are their any extra letters in the model number?

Curly cord means it's one of the original ones. Bryston's reliability is legendary (the new ones have a 20 year warranty.) It's normal for them to get warm. If you can leave your had on it comfortably for 10 seconds or more it's heat output is normal. As an aside if you ever do need to get it serviced Bryston is a dream to deal with and their service is extremely reasonably priced and very fast. Wonderful people.

I don't know what it's power output is at 6 ohms (amps are usually rated at 8 ohms and sometime a 4 ohm rating is also provided) but Brystons are great at driving difficult loads. What are the speakers?

I've heard good things about the Heil tweeters.

if you give the exact model number, I can help. I have a buddy that works for bryston.

The curly cord is a dead give away. It IS a first generation, no need for further research.

the power output is 290 watts @ 6 ohms.

heat output.. too many variables in play.