Uh no sorry...all I know is of all the support threads I've read for Project64 I don't remember a single one mentioning automatic shutdown. I do remember something about the hardware cooler for one guy's system being too weak, and they had automatic shutdown while trying to emulate something else. I just no this isn't really about the N64 as it is something intensive maybe Project64 tried doing.
Also GoldenEye was designed to be more system-intensive, so that'd explain that. There's another emulator called 1964 that comes with a much less intensive RDP.
http://1964emu.emulation64.com
The graphics will suck, but if that works for you I know how to fix that because there's a GPU based off Rice's Daedalus that shouldn't be that more intensive.