XBox 360 sleep timer?

I have an XBox 360 and I fall asleep every now and then. There's a sleep timer for the television and I wanted to know if the XBox also turns it off when it is switched on?

No, the Xbox 360 can't be controlled from a TV. There's also no such thing with Xbox One, because then it's the other way around. However, you can activate a sleep timer in the system settings of the 360. I think it lasts up to a maximum of 6 hours.