It is doable, but it's not going to be easy. You are going to need a microcontroller, and a good bit of time debuging the program and trying to get it to work exactly as you said.
An easier way to do it is to get rid of the touch screen. Use a simple 16x2 LCD, display the time on one line and the temp on another. Just solder in regular push buttons to bypass the push buttons already in the xbox. If you get the menu on the TV it's plugged into then there is really no reason to have the menu displayed on the LCD screen (this would take months or even years for an expert to do).