Need Help! My Class A Amp Is Running Very Hot

If you can hold your hand on it for 30 seconds, then it's not that hot.  Still, it's best to talk to the manufacturer/distributor if it really concerns you.

IF it is an used unit, make sure it is a 115v model ( not a 100v Japan model ) if you are in US otherwise a transformer is needed!

Read the paragraph under ’PROTECTION CIRCUIT’, on Page 1 of the Luxman AX590 manual: https://onahighernote.com/oahn/wp-content/uploads/2015/01/L590AX.pdf Luxman probably knows, how hot is too hot, for their product and have taken precautions.

IMO it probably is running as it is designed to run.  I have a Luxkit amp that runs hot, very hot to the touch so you wouldn't leave your hand on the unit and it has open vent slots but small heat sinks.  The kit has been around 30 years and works fine, sounds fantastic also.  One of the best sounding amps I have ever heard or built myself.  Oh course mine is slightly modified by me!

BTW the Luxman will wipe the floor with the First watt amp so I wouldn't even consider that move.

Happy Listening.

Perfectly normal. The amp has over temp protection. If it were abnormal it would be shutting itself off. This is what class A amps do.