2 day old MacBook Pro 13" run extremely hot

Go to about this mac, and is it the Mid-2012 Model?

Your 'problem' is that the game you are playing is a very CPU/GPU intensive application and will be the cause of the heat. This is not unusual. The truth is that Macs are not designed for games and PC's are much better in that regard.

Download istat menus and install it:

http://bjango.com/mac/istatmenus/

Open Activity Monitor to ALL PROCESSES and CPU set to display values from high to low.

When your MBP heats up, post images of both for inspection.

Ciao.

It is the game that is the cause of the high temperatures.

There are two things that trouble me. One is the temperatures are higher than I feel they should be. It has been my observation the temperature in the mid 90°s c is 'normal' for games. Two, the reason may be that the fan should be running as the maximum speed of 6200 rpm, not just 3596 rpm. I find it to be suspect.

You could run that Apple Hardware Test to see if it develops a fan fault but the prudent option is to take it in to an Apple store genius bar. Have them check it out and bring the image documentation with you.

Ciao.