Well, after looking at this issue I think I have come up with solution.
At least, my tab looks like it's back on track... though, to say for sure I would need another couple days of testing.
The problem is not runaway wild application on a background but battery control circuit. This chip reports to OS much smaller battery capacity as it is for some reason. I will not go into details but here is what you need to try:
Flash stock kernel (may be custom kernel is not the reason for bad chip calibration and I'm 90% positive but just to be on safe side). You don't need to do factory wipe in OEM recovery for our purpose.
You also don't need to wipe batterystats.bin or use "Battery Calibration" apps from market (which does exactly the same wipe just in more end user friendly way). This wipe serves no other purpose then refreshing your usage statistics.
You also don't need to drain your battery all way down... nice, this way you don't have to wait for too long.
Well, here we go:
1.Drain your tab battery upto 2 %
2.take a old credit card and start to pull of back cover
3.start from the edges and pull the side bezel that is all around
4.that way your bezels will be pulled that is attached to back cover
5.You will see the area where the battery is attached to device that is at the bottom
7.deatach it using big screw driver when you will pull off the wires which are very tiny in size the black connector will also come of
8.deatach and leave it for 12 minutes
9.place the back cover in place
10.Charge the device fully and it can take upto 5 to 6 hours
Thats it your Galaxy Tab is alright and working perfectly now
Note:1.i will note be responsible is you broke your tab or if anything goes wrong that should note be if you do it carefully
2.if you dont no how to deatache your battery from device from above steps then search on youbtube:"how to replace galaxy tab 3 battery"(the tutorials will be for replacing your battery but dont replace battery just deatach by watching the video)
Click thanks button if I helped