I would never leave my amp on all day, solid sate should not take to long to warm up as it is solid sate. I have a pair of channel island mono blocks they have no power switch just on or stand by so its stand by until its time to listen but they never run hot. Tube amps or pre amps usually need about 20 to 30 minutes to get to where they sound good. I had an old HK Citation 16s for 18 years never left it on and it finally needed service after all that time. Leaving your solid sate amp on for 4 or 5 hours continuously should be ok but I would turn it off after you are finished with it.
