Your amp needs some air flow & I'm guessing from your description that the back of the shelf is up against a wall? If not, I would remove the back of whatever you're using to get some flow thru. I would think the easiest thing to do would be move the rack away from the wall. If it is against the wall, then some holes in the shelf itself would be beneficial, provided you don't compromise the strength & integrity of the shelf. Also consider holes in the sides of the rack.
I keep my amp on the top shelf of my rack so it is completely exposed to air on all sides & it sits on isolation devices so there's some air flow underneath too. I have an old wooden rack that has been beefed up to support 500 lbs. of gear. I've had a Pass 350 & Threshold S300 up there at the same time.
One more thing you might want to consider is a low speed fan that operates on batteries. You may be able to position it behind the amp w/o drilling any holes just to get some air moving. The same holds true for an electrical fan like something out of a computer but noise may be a factor. There are some fans designed for low speed/low noise that may work ok.
I keep my amp on the top shelf of my rack so it is completely exposed to air on all sides & it sits on isolation devices so there's some air flow underneath too. I have an old wooden rack that has been beefed up to support 500 lbs. of gear. I've had a Pass 350 & Threshold S300 up there at the same time.
One more thing you might want to consider is a low speed fan that operates on batteries. You may be able to position it behind the amp w/o drilling any holes just to get some air moving. The same holds true for an electrical fan like something out of a computer but noise may be a factor. There are some fans designed for low speed/low noise that may work ok.