On both occasions, the load on the video card shold not have been that severe at the time the shutdown happened: 1st time in Whiterun, preparing to use the Armor crafting table, 2nd time in Riverrun, in the traders shop, preparing to sell some stuff. Now that I think about it, on both occasions I was in or going into an inventory screen.
The 1st time, I tried again next morning, and it worked, worked fine for about 5 hours that day, as much time the next day. 2nd time it shut down less than an hour in to the game, after a few hours off, it seems to be OK (it is booting up as I type).
Card is an ASUS HD5770, about a year old. I do run "ASUS Smart Doctor" in background - did NOT hear any temperature alarm. Fan sounded normal (as far as I remember anyway) - which is NOISY - I have fan speed controls set for 35/45/50/55 C for Slow/Medium/Fast/Fastest speeds. I'm using older drivers ver 11.6. Skyrim patched to ver 1.4..whatever
Sitting in windows desktop, GPU temp reads 34C according to S.D.. I have to minimize it while playing Skyrim, else I see a flickering section where S.D. is - so if I quit out of Skyrim and try to check temp, it takes several seconds. But doing that, I typically see temps less than 50C (and cooling fast)
Should Smart Doctor be sounding an audible alarm if card goes overtemp?
What temp should card be able to run at?? I would expect 75C or better, which is where I set the alarm at
Does it mean card is shutting down before reaching 75C
I believe that the S.D. temp reading is correct, as it matches that in the Catalyst Control Center
Any suggestion appreciated

