While Microsoft doesn’t explicitly say it’s okay to do so, there’s good evidence that it is in fact perfectly safe to run your Xbox fully powered overnight, and even longer. There are zero warnings or suggestions on any of Microsoft’s official Xbox support pages to periodically turn off the console. In all likelihood the Xbox Series X and Xbox Series S were designed to run for years without needing to be shut down, considering their predecessor, the Xbox One, was built to continuously run for ten years straight.
Of course, this comes with a caveat. One of the main fears people have concerning a console left running too long is overheating. The Xbox Series X and Xbox Series S run on sophisticated AMD chips with very tiny, sensitive components. These components, as well as other parts of the Xbox hardware, or game discs left inside the machine, could in theory be damaged if the internal temperature of the console runs too high. Given that Xbox doesn’t suggest you turn off the console, it’s likely it was designed to continually regulate its temperature, mainly with the use of its fans.
However, you need to make sure you place your Xbox in a position where it can ventilate itself properly while turned on. Make sure nothing is blocking the console’s built-in vents – in fact, don’t place any objects directly against it at all. Xbox Support suggests leaving 4-6 inches of space around the console, and not placing it in a confined space or near a warm surface. This will allow hot air to dissipate before it can do any damage to your console.