Laptops can generate a lot of hot air.
A collegue of mine had a Pentium IV laptop with the air vent on the same side you would use an external mouse. The air was so hot it was very uncomfortable using the mouse! But the machine never locked up or shut down.
So, it's not necessarily overheating that is causing the lock ups on your machine.
Have you recently installed any new software or changed any settings? Are you using an external USB mouse or any USB devices?
As it's a new machine I assume it's under warranty - might be worth getting them to look at it.