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It's a step down transformer so some hum and warmth is expected even with the amp off, but if it's really hot to the point you can't hold your hand to it it might be faulty and fire danger.
Warm is usual, but shouldn't cause audible hum(I have 3 of the ac adapters from jds). If the hum is clearly audible when you are sitting on the chair, you may consider contact jds.
I leave mine on 24/7 as per the manual. The adapter is very very lightly warm to the touch I can't hear anything from a few inches. I feed it conditioned 110v.