My buddy and I both shoot with the 1Ds Mk III, and they have served us well, except for his long exposure (30 secs & longer) high ISO images (1600) have a magenta shadow in both right corners. Mine doesn't. Canon is saying that it's an anomaly due to heat being generated by a couple of elements near the sensor, and that they've been able to replicate this with other bodies in their shop. Question to all that use the same body, have you seen this on your images?
Yes, mine had amp glow too. Most visible at and beyond ISO1600. In my case it didn't need a long exposure to make it visible. Although long exposures make it worse of course. It's a feature. All the 1Ds3 I have used/owned show the same behavior.
Check these guys, they can add a cooling system to the 1DS-mk3, but you lose the dust shaker. They also do full astro conversions. They are near my house and I spoke with the guy who does the work in a Lab at the University of Utah. He can also precision align the sensor for accurate infinity focus.
I have never had any work done, but if I ever had a spare body I would probably have the full astro conversion.
I also get the glow and if you ever take a shot at clear blue sky (dust check) at f22 and run autolevels, you may see a lot of sensor artifacts you never dreamed of.