Can someone please explain the error code 4SNS/1/40000000: TMOP-127.875 and how to fix the problem?

Are you having any problems? Why did you run Apple Hardware ****?

From

http://www.cnet.com/news/how-to-invoke-and-interpret-the-apple-hardware-tests/

that would indicate a bad sensor on one of your memory modules or riser board:

In the case of a sensor error (4SNS), to determine what type of sensor is being referenced, check its first letter, which should either be "I" for current, "T" for temperature, or "V" for voltage.

Then check the second letter against the following list to see what component it refers to:

A: Ambient air sensor
B: Battery
C: Central processors (CPU)
D: DC (direct current)
e: PCI-express slot
F: FireWire port
G: Graphics processor (GPU)
H: Hard disk
h: Heat pipe (heat sink)
L: LCD display
M: Memory or memory riser boards

I would first install a temperature monitoring app like Mac Fan Control

http://www.crystalidea.com/macs-fan-control

to see of you can find a bad sensor by the reading for memory riser board.

Do you have a MacBook Pro as indicated: MacBook Pro, OS X Yosemite (10.10.5)

Since this is the Mac Pro desktop forum

The most common reason for uncontrolled shutdown is overheating.

You should make an appointment at the genius Bar at an Apple store for a free evaluation, if available to you. They are good at power problems and physical problems like fans not working properly.