Are you sure you are not overheating? What are your temps. Even when running on the power you have your battery as a back up. What you are describing sounds like it will not overheat at the decreased performance level but when plugged in running at max performance it does overheat.

 

Sorry I'm not very good at describing. My temps usually never surpass 60c while on the power supply (gaming).
Another example I have of it shutting down is when I try to run an uploaded video through Windows Media Player and my laptop shuts down almost immediately. This only happens when I am plugged in but when I'm not, I can play the video.

 

Remove the battery, run on A/C power and see if the problem persists.

 

Download this http://www.cpuid.com/softwares/hwmonitor.html and post your temps, maybe your video card is overheating?Try changing the power settings to power saver while plugged in and see if you still shut down.

 

• Okay so I tried playing a video on Power Saver mode while on A/C power and thankfully it works! The shutting down did not occur.
• I tried running a video on High Performance settings with the battery removed while on A/C power and my laptop still shut down.
• Here are my temps while on Power Saver mode and on A/C power with a video running in the background.

Hardware Monitors
-------------------------------------------------------------------------

Hardware monitor ACPI
Temperature 0 58°C (136°F) [0xCF0] (THRM)

Hardware monitor Intel Core i7 820QM
Power 0 13.78 W (Processor)
Temperature 0 56°C (132°F) [0x2C] (Core #0)
Temperature 1 56°C (132°F) [0x2C] (Core #1)
Temperature 2 59°C (138°F) [0x29] (Core #2)
Temperature 3 55°C (131°F) [0x2D] (Core #3)

Hardware monitor NVIDIA GeForce GTS 360M
Temperature 0 38°C (100°F) (GPU Core)

Hardware monitor Hitachi HTS725050A9A
Temperature 0 36°C (96°F) [0x24] (Assembly)

Hardware monitor TOSHIBA THNS064GG2BB
Temperature 0 34°C (93°F) [0x22] (Assembly)

Hardware monitor Battery 1
Voltage 0 12.57 Volts [0x3119] (Current Voltage)
Capacity 0 100544 mWh [0x188C0] (Designed Capacity)
Capacity 1 79002 mWh [0x1349A] (Full Charge Capacity)
Capacity 2 79002 mWh [0x1349A] (Current Capacity)
Level 0 21 pc [0x4E] (Wear Level)
Level 1 100 pc [0x64] (Charge Level)

 

• Okay so I tried playing a video on Power Saver mode while on A/C power and thankfully it works! The shutting down did not occur.
• I tried running a video on High Performance settings with the battery removed while on A/C power and my laptop still shut down.

• 
  
  It would appear the problem is with the AC adapter.

 

Have you cleaned your computers heat sinks for dust lately?
Also go into advanced power options for high performance and make sure cooling is set to active not passive.
Heres how you get there (i don't have this option on my desktop)

 

Mmm I don't have a cooling passive option, but it's set to maximum instead of minimum. Also this laptop is pretty new and I have used compressed air to clean out my vents just in case the problem was dust. I'm not sure if that's enough.

 

Tr running this and monitoring the temps until it turns off http://www.overclock.net/downloads/138142-orthos.html

 

It would appear the problem is with the AC adapter.

I was assuming the same thing. Would you happen to know how to go about fixing the problem or would I have to contact Toshiba directly and let them know that I have a faulty A/C adapter?

 

Things like that you don't fix you just get another. However if still under warranty they should replace it for you.