I went back and looked at the tool you were using to check your temperature.
If I'm not mistaken, it looks like it's checking the temperature of your HDD. Which at 44 degrees, is warm.
However, since CoreTemp showed a temperature of 0, I'm thinking there's something wrong with the thermometer, or CoreTemp is trying to read the wrong one. You could also check Realtemp, to see if that gets you any other result.
My guess is that it is shutting down due to heat, I know that seems to be a fading possiblility, but it seems we don't have the right information about your temperature (It also showed an A10 in that screenshot, with 44* Celcius, but you don't have an A10, so that is very odd, the A8, which you have, showed a temperature of 0.).
The fact that you have an AMD chipset in this laptop makes it more likely that it could be shutting down due to heat somewhere around the 80* - 90* Celsius Range.
You can check the temperature in the BIOS, it usually shows a little warmer than it is.
I would try another tool, perhaps even getting MSI Afterburner, and RivaTuner, and running it with Minecraft, that way you can watch the temperature of everything, and see what hits what before the computer restarts.
Another thing:
Does it shut down when plugged in, or only when on battery? (Sorry if this has already been asked.)