I don't think anything unusual is happening in your case. Just making some general observations:
The heatsinks provided are probably good for about 20C/W dissipation; meaning the heatsink temperature will rise 20 degrees C above ambient temperature per W dissipated.
Ambient in these situations (a hot day, no fan, heatsink in enclosed or semi-enclosed area) is best taken at 50C.
At 10W out and the PA 50% efficient, each transistor would have 5W to get rid of on constant keydown or about 2.5W during morse sending.
So that makes 20C/W x 2.5W + 50C = 100C (burn your finger temperature for sure)
This is a worst case example as ambient is high (you may have better air circulation around the heatsinks and a cooler room), the power may be lower, and the PA may be more efficient. But it gives you an idea of how hot the heatsinks may get. With no fan, the stock heatsinks are not good for more than a watt or so if you want the transistor and heatsink to stay at "just warm" temperatures (less than 60C). And no way would they be good enough for digital without fan help. Bigger heatsinks will allow for cooler tempertures, or you can run a fan on them as I think many do here.
Remember the transistor tabs need to be insulated from grounding through the heatsinks/housing.