Is anyone aware of what the operating temperatures would be for a situation where the Mark III would be taken to an elevation of almost 4 km (2.5 mi) and used straight out of the bag?
Example:
July, mountain top, sunrise, 4 km / 2.5 mi above sea level
In the past year I used a Mark II in Norte Grande- Cile at 4700 mt altitude (2-3 degrees) just came out from the heated car. No problems. Nor Nikon D700.
If you're hiking/climbing up, should be just fine since it'll adjust somewhat to the ambient temperature while you're climbing. Unless you're dealing with freezing temperatures, in which case you definitely need to make sure it's at ambient before putting the battery in (need to keep them warm!) and using it.
Is anyone aware of what the operating temperatures would be for a situation where the Mark III would be taken to an elevation of almost 4 km (2.5 mi) and used straight out of the bag?
I have no idea how the camera would do, but if you mean going straight from sea level by plane or land humans don't do well at all. Google "altitude sickness" and read up on acclimatisation. It can be fatal.
At a rate of altitude increase safe for humans (days), your camera will have time to equalise its temperature with the outside. The pressure, of course, is instantaneously equalised, since your bag is not a pressure vessel. I think we can assume that a 5D Mark III will not explode at 4000m. In fact I'd guess it's been built to handle shipping by air at 10,000m.
I just wanted to drop in to say that I used the 5D Miii on the summit of Kilimanjaro, both for video and stills. Worked like a champ. No troubles at all.
People have gone a lot colder than 0C (I think there's a thread somewhere), so the main problem is humidity. If it's clear, the humidity is probably low enough. If you are in clouds/fog, it's too high. At night and early in the morning stuff collects dew if it cools below the dew point by radiant cooling. Keeping the camera in a bag or slightly warm should prevent dew. Live view or video mode will probably generate enough heat to keep the camera dry. If you bring the camera into a warm place (a car, or a building) after being outside in the cold it will probably also collect condensation (same as dew), which is bad. To avoid this, keep the camera in a bag until it warms up so that the warm humid air doesn't condense on it.
There are ways altitude can cause issues, but not the kind of altitudes you are discussing. In extreme high altitudes, outgassing of silicones, lubes, plastics and the like can redeposit themselves where they care not wanted. You do not want them to deposit on your sensor or lens elements. That's why special modifications are made for equipment going into space. Part of my job used to be making sure that components used in spacecraft met outgassing specs.
Moisture is the enemy, rapid temperature change from warm humid to cold is the worst, since moisture condenses inside your camera. Taking a very cold camera into a moist warm room will condense moisture on the outside of the camera and lens where it is much less likely to be a problem.