Laptop randomly shuts off with no warning. Please help!

OS Version: Microsoft Windows 7 Home Premium, 64 bit, Toshiba Satellite A665 series
Processor: Intel(R) Core(TM) i3 CPU M 370 @ 2.40GHz, Intel64 Family 6 Model 37 Stepping 5
Processor Count: 4
RAM: 3890 Mb
Graphics Card: Intel(R) HD Graphics, 1721 Mb
Hard Drives: C: Total - 463566 MB, Free - 282592 MB;
Motherboard: TOSHIBA, NWQAA
Antivirus: Microsoft Security Essentials, Frontier Secure, Malwarebytes Anti-Malware

Problem
So my computer keeps shutting down. I just bought a replacement battery for my computer so I don't think it's a battery issue. I read some previous posts abut Windows 7 not reading their battery status correctly and shutting off the computer with a 50% battery message. However, If my computer shuts off with the battery attached, I am still able to turn on the computer, run windows startup, and load programs. Similarly, my AC power adapter is still able to charge my computer.

I don't use up a lot of memory either. I ran my virus protection software and it said that my computer was clean. Additionally, my computer doesn't seem to be overheated and there's nothing blocking the fan.

Any suggestions for narrowing down the problem? It started a few days ago.

Okay, I'm going to include a screenshot of what Speccy said regarding the computer's temperature.

Is the temperature listed too hot/abnormal for my computer? I put my hand next to the vent and it feels warm, but not hot. Before the computer shuts down, it does make a whirring sound and blows out hot air.

If the computer is overheating, what's the best (and preferably inexpensive) way to cool it down.

I also don't know if this helps but when I open Task Manager, CPU usage fluctuates between 40-65% with Physical memory being at 78%

I had to take my laptop in, but it definitely decreased the temp from 150 to 110-114 so that helped a lot. Additionally, I had a lot of programs that started in the background and I disabled the ones I didn't need. :] Thank you so much for your help!