I am having the same trouble with my lenovo k3 note ,its not a big matter as everyone said...I fixed this problem my self in a few min..Probably phones with li-on batteries are having such problems. I will tell you the steps which I had followed to fix my phone
1. I removed the battery first and Make the phone and battery alittle warmer by using a cotton(even a blanket)
2. After that I placed my phone in a blanket which will make the phone warm for a while.
3.And I used a multi charger to charge the battery directly for about 30 min..The I switch on the device ,then I found 3% charge on the device ,first I thought the problem is didn't solved yet....
Then I charged the phone using a charger and used it for while during charging... Now I am not finding any "low battery heat issues"... Its works fine...Try out these guys..I hope it will work for you too..