I was wondering if there was any empirical evidence that placing the xbox horizontally/vertically facilitates better dissipation of heat w.r.t the other orientation? What is the best strategy (apart from not using it heavily or using external cooling) to ensure the console does not overheat
The vents on the Xbox 360 are on the sides, when it is sitting horizontally. You'll get the best airflow if you have it sitting horizontally. That being said, the heat is largely generated on the bottom of the machine, when it is horizontal. For best heat dissipation, you'll want to have it sitting horizontally, with it propped up slightly so the bottom can breathe.
Another side effect of standing it vertically is that it has a greater chance of scratching disks. You'll mitigate that by having it sit horizontally.
I can't add comments yet so I am going with an answer. I think Michael Herold meant to say It is best to have it sit horizontally with it propped up so the bottom can breath. I also recommend this setup. Also if you have a TV stand with shelves I would recommend not putting it on a shelf as the pocket of the shelf also accumulates heat. Set it on top of the TV stand or on a table/stand beside the TV stand so it is in an open area.
I don't think the orientation is as important as how much it can 'breath'. Make sure that heat can plume up and away and a cold draft be drawn in. Dont put it in a container with just a cable hole in the back. Ideal is an upper opening and a lower opening so that the heat generation can create a natural convection current.