The game is likely running your video card much harder when sitting on the menu than in the game. That in itself will make it run hotter and if your card isn't able to cool itself properly for whatever reason, it can result in the PC shutting down to prevent damage.
You can do a few things for this.
One, check to see how hot it's getting on that screen first.
Download and run HWMonitor from: http://www.cpuid.com/downloads/hwmonitor/1.20-setup.exe
Now start the game and let it run several minutes. Then exit or alt-tab out and see what the highest temperature is that was reached for both the gpu.
If it reached 85C or higher, I'd suspect it's an overheating problem as described above.
If you have a desktop model computer, unplug it from the AC power, open it up, and using a can of compressed air, clean out the video card's fan and heatsink assembly. That's often all it takes to restore proper cooling to it
If it's a laptop model, unplug it from the AC adapter, remove the battery, and open all the compartment doors you can to expose as much of the inside as you can. Then using a can of compressed air, carefully try to get all the accumulated dust out of it. Blow into the exhaust and intake vents as well. Run with a cooling pad beneath it while playing as well.
You can also try limiting the FPS in the in-game menu. Set the foreground to 60 and the background to 8 to start.