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Since its a new computer, just call Gateway and have them fix it under warrantee.
Should you decide not to mess with corporate hooligans, here is my advice:
Spoiler:
Sounds like your processor is overheating.
To test if this is definitely the case, do the following:
Download Speedfan, install it, configure it with logging enabled, and have it run in the background at all times. When the computer decides to shut down, you should hopefully have a log of the temperature of your processor in the SpeedFan installation directory up until the last second of operation. When your computer is all rebooted, go into the installation directory, and search for a dated .csv file. This should be the log. If you restarted SpeedFan before going into the directory, the log file should have an "-0001" at the end of the file name.
Anyways, check this file at the very end to see if there is any significant jump in temperature at the end.
If this is indeed the case, demand that Gateway send you a bigger fucking fan for the CPU.
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