the cabinet on the top temperature is 28C which I think is just a little warm but acceptable but when I put my hand on top of the plastic vents (over the heat shrinks) it is extremely hot, way over my thermometer maximum temperature of 50C
To add perspective, my Pass XA25 amp operates in class A and consumes an amount of power (240 watts at idle) that is very similar to yours. The XA25 is stated to be designed such that after it warms up to a stable temperature its heatsinks will be about 25 degrees C higher than the temperature of the room. (Elizabeth makes a good point about the significance of room temperature, btw. Each degree of difference in room temperature will make the same difference in the temperature the amp stabilizes at, following warmup).
So under typical room temperature conditions the heatsinks on my amp will approach 50 degrees C. Very significantly, however, in contrast to yours the heatsinks on my amp are on the outside of its cabinet:
https://www.passlabs.com/amplifier/xa25#lg=1&slide=8
The heatsinks on my amp also appear to have much greater total surface area from which to radiate the heat than the heatsinks that are inside of your amp.
So, again, it seems to me to be very possible that what you have described is normal, although I am not in a position to be certain about that.
Regards,
-- Al