Pc goes to stand by mode while playing bf2042

Stand by mode normally wouldn't be forced by any legitimate application's behavior. If it's going black screen and completely unresponsive, that's not standby that's a crash. So I'm going to divvy my answer on two different assumptions:

If it's crashing start with the Event Viewer and look for any hardware events that coincide with when it blacked out. There will usually be an administrative event with the crash code you can then research to diagnose which driver/hardware is failure and start with an update to that component. If possible, test a substitute. 

If it's actually going into standby rather than a DirectX or Blue Screen my first thought wouldn't be hardware (temp/power) related but OS/kernel. There might be a driver in use with BF2042 that your other games aren't utilizing that's triggering it. Firstly, I would check if all my drivers are up to date (check Windows update, your PC manufacturer's driver website, don't touch any BIOS updates, pay special attention to chipset drivers,graphics card, etc.) 

From there troubleshooting is a matter of taste in what you want to start with. Personally, I would start by running these tasks in Command Prompt as an admin, they're slow but thorough: 
1. DISM /Online /Cleanup-Image /ScanHealth This will check and report any issues with the Windows image. If no corruption is found, go to step 3. Otherwise proceed to step 2. 
2. DISM /Online /Cleanup-Image /RestoreHealth This will repair the image using Windows support services
3. SFC /scannow This will use the image you've just checked/repaired to compare against existing system files and replace any that have been corrupted. 

You can also attempt to use the built in Event Viewer in Windows to check the administrative events tab for any errors that coincided with when the stand by happened. If you find an event that coincides, research the error code for a better idea of what's causing the lockup. However in my experience this has yielded less steady results than a blanket system check when the culprit is OS/kernel rather than hardware. You may find the culprit, or you'll get no event, or you'll get an event with a vague error that means essentially nothing. 

If all else fails, the ultimate OS/kernel fix would be reformatting your device and starting over.