I just went over and tested my BAT VK-50SE. The top plate has a large center section (maybe 75%) where many ventilation slots have been machined. Of course, this is right above the 8 x 6H30 valves, so this is where the heat is generated.
If I put my hand on the solid plate area outside the ventilation area, the metal is only slightly warm. On the ventilated area, the metal is much hotter - particularly towards the rear of the case. But I can put my hand on this area for some time - it's not so uncomfortably hot that I have to remove my hand.
Mine is on the lower shelf of a two shelf PolyCrystal rack, but there is a big gap (9 inches) between the amp and the top shelf where the CD player is.
Over the 5 years that I've had this setup, the warmth reaching the top (heavy duty) PolyCrystal shelf and the weight of the Sony XA777ES has caused the shelf to bow somewhat. Had I known that this would happen, I probably would have put the preamp on the top shelf.
I'd also like to know what you thought of the 52SE.
Regards,