This is bad for EVGA. My 1080 FTW exhibited similar issues, but it was only the fan that ramps to full speed as soon as a game or Precision X/Afterburner is launched. I've never had the screen go black or any errors. I'm not sure if your cards showed the fan speed RPM in Precision X or GPU-Z? Mine fails to report any fan exists (0%) despite both going full speed! I've played games all day at ultra settings and the card has been perfect, other than the fan issue which requires a reboot to stop it going at full speed.
My replacement arrives Wednesday, fingers crossed it's all good, but I'll try those tests you guys performed and if it's doing the same it's going straight back to Amazon and I'll buy an Asus. I always buy Asus products and think there's a reason they are now expensive. I thought I'd try EVGA since they had a ton (close to 500)of great reviews in Amazon, the old rule "fool me once, shame on you" applies.