Pretty sure my SWR Baby Blue owner's manual warns against leaving the amp on for extended periods of time with no input signal. IIRC, the manual indicates that doing so could cause the amp to need to be serviced.
Well the amp in question here is actually an SWR Super Redhead. I got mine second hand, so I never had the manual, but it might say the same for mine. It's a tube preamp, but still has solid state power, and I'm assuming that's where most of the heat would be generated.
How about leaving a DC Brick on, cause if my amps on, the pedals are powered up too. The question is pretty much answered already, but I don't know man, could be somehow different.