Yup, syncing stuff will definitely use/drain battery... especially if you're unaware something is syncing or perhaps what's being sync'd are corrupted files. Also, and I don't know if it was fixed yet, Facebook was tearing up some peoples battery time, even though it didn't show it in the battery stats percentage, so if you use Facebook and you have some strange battery issues, try disabling it to see if it makes a difference.
I use
Debloater (free) to turn off/disable some unnecessary system apps. I don't know if it runs on MM, but it does on KK and LP. You can also run
Package Disabler Pro to do the same thing, and it's probably easier to use than Debloater, but then it costs $1.95 on Playstore.
My phone never runs hot and I've had it since Jan 2015. It's still on Kitkat by choice. If your phone ever runs hot for any reason, something abnormal is going on.
Good luck with your new phone... it has a lot of good stuff in it... not withstanding that great S-Pen! It's the last "real" Note in the series!