This is what canon has to say about this.
http://www.canon.co.uk/Support/Consumer_Products/products/cameras/Digital_SLR/EOS_5D_Mark_III.aspx?faqtcmuri=tcm:14-731490&page=1&type=faqHaven't found out the temperature when the overheating icon will appear, never saw that thing in the first place to be honest.
Just tested the camera in the morning.
Startup with magic lantern, no recording, no raw:
Global draw on, zebra's on, histogram on RGB.
5d3 was on a rig, so no heat from my hands/body
shot with external monitor.
Room temperature was 20 °C
All temperatures came from magic lantern. i don't have an infrared meter.
Startup: 19 °C (a1ex, difference of 1 °C with room temperature)
after 20 seconds 24 °C
1 minute: 29 °C
2 minutes: 33 °C
4 minutes: 36 °C
8 minutes: 47 °C
And it kept there for 30 minutes, quit test after that.
let it cool down a bit and went recording continuous
Recording H264 codec:
startup 36 °C
1 minute 43 °C
2 minutes 47 °C
4 minutes 49 °C
8 minutes 49 °C
quite stable
Raw 1080X1920 (single take)
startup: 34 °C
right after i put on raw in the menu: 42°C
10 seconds 44 °C
20 seconds 47 °C
30 seconds 47 °C
40 seconds 47 °C
1 minute: 47 °C
2 minutes: 48 °C
3 minutes: 55 °C (orange)
4 minutes: 55 °C
5 minutes: 58 °C
6 minutes: 58 °C
6.30 min : 60 °C (red)
7 minutes: 62 °C
8 minutes 60 °C
9 minutes 59 °C
10 minutes: 59 °C
It kept stable from 6.30 minutes, 60/59 constant.
checked if there was a difference in heat with higlights or darks but no difference. (this included zebra striping galore)
Raw
without monitor:
startup: 33 °C
right after i put on raw in the menu: 33°C
10 seconds 40 °C
20 seconds 40 °C
30 seconds 40 °C
40 seconds 40 °C
1 minute: 43 °C
2 minutes: 45 °C
3 minutes: 48 °C
3.30 min : 54 °C (orange, went straight up from 48 to 54)
4 minutes: 54 °C
5 minutes: 56 °C
6 minutes: 56 °C
7 minutes: 59 °C
8 minutes 62 °C (red)
9 minutes 69 °C
10 minutes 70 °C
kept stable 70 °C after that.
After this i did another test with the monitor again, but that gave quite similar results as the earlier test.
tried putting in the monitor after various minutes shooting without, cooled down a bit (5 °C)
tried all tests again with alot of different shots (starting, stopping) but didn't really affect the heat.
it seems that the monitor "cools" it for about 8/10 °C