Does this happen in other games? Sounds to me like a driver crash issue. You might need to check if you have new motherboard bios or GPU bios, check those first. I'd rule those out. Then if your fine there, the only way it'd black screen is if there's 1. A defect with the card or 2. Some issue with drivers. Temps could be an issue, but not relating to the GPU core temp, it could be VRM or memory temps that could cause that issue. I'd make sure the card has everything there, make sure the VRM's have a thermal pad on them.
The only black screens I've ever gotten were on my 580 when I overclocked too far, and not related to temps, the card just blacks out....I believe its just an issue with stability.... Maybe try downclocking the memory a tad and try again?
I've never had an issue with JC2, always ultra graphics, totally maxed out with my 580 and with my 670, gameplay is great!