Well. I guess you found manual for old Kinde Fire (1st generation). Maybe for Kindle HD it's looks different. Interesting, I can not find similar manual on Amazon.com (with operating temperature range) for Kindle Fire HD 8.9". This is a red flag.
RE: Custom battery monitor: For me no sense additionally to calibrate battery at this point. Let's left it to Amazon design team. They produced it, they should to fix it.
Just think about it - an installation of additional software will interfere
with original problem. It do not help.
It's clear now, in this temperarure range (10C-15C) one of two (or both ) problems are possible:
1) The KIndle HD battery has a problem or
2) Build-in Kindle's Fire HD battery monitor does not operate correctly!
Do you agree, Sirmaru?