New iMac 27", will just shuts off.

I recently just received the new 27" iMac. Have been using it for about 4 days. When I'm not using it, I normally let it run on screen saver mood for about 3 mins and then sleep mode after 15 minutes. However, after the computer goes to sleep, I try to turn it back on, it won't start. I'm not sure if the computer is still asleep (and my keyboard/mouse) is unable to wake the computer up or the computer is off.. I then will try to turn it back on by using the on button but it will not start at all. I have to wait for about 5-10 mins to turn it back on and I have to press the button a few times before it does. Is this the same issue with the computer shutting itself off because of the computer overheating?