Bryston 4B gets HOT. Should I leave it on?

Sean's advice is on the mark. A good friend has the same model Bryston amp as yours (he's using his in a second system), and his amp never gets terribly hot, even when being driven hard. While it may be easier on the internal components of solid state amps to leave them turned on, it is NOT good for those components to be continually exposed to high heat levels at idle.

You could send your amp immediately to the Bryston repair facility in Vermont, but you might first seek the advice of James Tanner, the technical expert at Bryston. You can send an E-mail to Tanner by going to Bryston's home web page, and clicking on the link at the bottom that reads "Technical questions please click here". On business days, Tanner normally responds to questions within 3-4 hours.

Until you get your amp checked, I'd recommend turning it off when not in use. When you plan to use it, turn the amp on about 20 minutes or so before playing music.

Yes, you could wait until the amp quits working to send it in for repair, but by then you may face a much more expensive process due to deterioration or failure of other internal components. Like the Fram air filter ad used to say: you can pay me now (probably cheaper), or you can pay me later (almost certainly to be more expensive after a major problem). I'd send an E-mail to James Tanner and ask his advice -- that costs nothing, and may yield some very useful information.