FYI the 5600 suffered from bearing lubrication issues and actually prefers to be overfilled, especially the early ones. If I remember right from years ago, I think one quart overfill was the general consensus.
Not that its the same transmission but my 4500 has Fastcoolers and I have upwards of 7 quarts in it and it runs no hotter than 200* even while towing heavy.