The temperatures are tolerable. At least in the numbers you showed me, I see not reason the CPU would shut down over those temperatures.
Well, if you bought a real cheap power supply, it could be that. But to prove that is going to be hard. Especially from where I sit. the fact they could not even be bothered to put a brand on that really scares me. The insides of that thing must be very close to junk quality.
I would suggest that you buy a better power supply. Toms keeps a list of power supplies sorted by what we call tiers. Tier 1 are great power supplies. Tier 2 is also good power supplies, but minor imperfections or just a bit less than highest quality parts might have been used. Tier 3 reaches the lowest point that I would buy from. It has some cheaper parts, and might have some imperfections that might limit your ability to overclock or otherwise push the limits of the power supply. Tier 4 is worse yet, and tier 5 is junk.
To find a power supply and see where it ranks on this list, Press CTRL-F, and then enter the brand name. Then look to see if something listed under that brand name matches part of the model and watt numbers. If not, search for the next time that Brand name is in the list, and each time you find the brand name, under it, again, look for something that has part of the model number and possibly the wattage.
Once you find a match, scroll back up slowly until you find the Tier header, and that will tell you the Tier that the power supply model is in.
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html