The screen goes black after playing The Sims 3 for 30 minutes

stivhatten​  Please provide a dxdiag.  Click Windows key-R, enter dxdiag in the run box, wait for the scan to finish, click "Save all information," and save the file to your desktop.  From there, you can attach it to a reply using the paper clip (Attachment) icon included with the other formatting buttons.

Please also let me know whether you've taken steps to limit your in-game framerates, AND confirmed that the limit is being respected.  To check, enter the cheat fps on , and a counter will appear in the upper-right corner of the screen.

Thanks for the reply!
Here's my dxdiag file as requested.

About the fps, I've only limited them through the Smooth Patch. I've recently set the limit to 30 according to some experiments done by others, but before that, my limit has always been 60 (and it has worked flawlessly). I will again play Sims 3 soon keeping an eye on the counter you mentioned, and I'll let you know.

stivhatten​  Interestingly, your dxdiag doesn't list any errors at all other than one system issue that might be nothing, so no Sims 3 crashes, no BlueScreens or other serious events that might have happened while you were playing.  And even if the game issue isn't generating errors, it's extremely rare to see almost no other errors unless their data is removed or can't be read.

On that note, are you using some kind of cleaner app that deletes temporary files?  If so, please disable or delete it, at least for now.

I do need that data though, or at least to know whether there are truly no Sims 3-related errors.  So please try again to play, let the game freeze your computer, restart, and then look for new errors in the Reliability Monitor.  Click Windows key-R and enter "perfmon /rel" without quotes, and you'll see a chart of errors and updates with a column for each day.  Today is on the right.

Look for an error that happened at exactly the time of your most recent Sims 3 crash.  If you find one, double-click it to see more details, then copy that info and paste it into a reply here.  If you don't see a new error, check back in an hour or so—the Reliability Monitor doesn't always update right away.

Your computer overall should be fine running Sims 3, and I haven't seen any particular issues on this class of hardware, although traffic on this site isn't all that high with respect to this game.

What system issue? Should I worry?

Anyway, today I tried to play again The Sims 3, but raising the fps limit at 60 (like on my old laptop and like most players do). The fps counter was on and it never went above 59. 
Unexpectedly, I played smoothly for two hours without any crash or black screen. Could be limiting fps at 30 the cause of this problem?
I'll play again in the next few days and I'll keep you updated. Maybe I was just lucky today.

stivhatten​  The one error in your dxdiag could be nothing meaningful at all, or it could be something, but the nature of the error doesn't make that clear on its own.  So there's no reason to worry based on that info alone, and currently no other concerning info of that nature.  The fact that the screen goes black while you're playing is probably more significant.

I doubt that setting the fps limit to 30 would cause the black screen, but the important question is whether it happens again.  And you can set a limit of 60 or 59 or whatever works for you.