I don't think you will have any issues.
I have a pair of STA-9 that have been on 24/7 for 3 weeks, and they are only slightly warm to the touch. (like a mild fever)
Your idling temperature may vary depending on your speakers and wire load.
The top of the case is used for heat dissipation, and it is barely warmer than my hand. A single amp in a contained space would certainly not feel cold to the touch, but you would not have a problem.
The DAC-9 would be even less.
I would place the STA-9 on top of the stack if you have a choice, and you would also benefit (heat wise) to find (if possible) some 1-1.5 inch rubber spacers, to put a little ventilation space below the amp section.
Something LIKE THIS
Also regarding of placement in the cabinet, the two components should be placed fairly low. This, allows a greater space for heated air to rise and allow cooler air (which will be lower in the cupboard) to ventilate.
If you have really low impedance speakers and run them really hard, you will notice more heat will be produced, but likely nothing of concern.