Almost all phones get a little hot when using them. It really depends on what all you have running. I have a habit of closing out everything when done using it. Below is what I do to all New Electronics I get. (Especially the first charge)
When I first bought my Note 3 (4 Days Ago) I used it and let the battery die all the way before charging it. 0%
Did the Gear that way to (Galaxy Watch)
Then I charged both all night (100%)
The next day, I used both products all day and night till about 3:30am.
I charged both again (they were at around 8% Battery left).
Next day they got even better. I did not charge them at all.
Used them yesterday and charged last night.
This morning I have used both and both are not hot and have over 90%.
There are a bunch of apps out there that run in the background and kill your battery.
Don't put a bunch of useless crap apps on your phone and power cycle your battery once a month
(That's letting your phone die all the way down to 0% and charging it up to 100% while phone is off)
I have the best battery life even without root. By the way, this phone is great without rooting (so far)
I'm sure one day I might root this one but for now. NO WAY....Its sick like it is.
Just try what I'm saying and I promise, you will see a difference.
Again, I do this with all my electronics and always have the best battery life.
Its okay when your phone gets hot. When I watch Your Tube vids for hours at a time, it gets hot.
The Otter Box doesn't help. Still, these phones can handle it.
I hope someone gets help from this post, I wouldn't take the time to type this if it didn't work for me and my friends.
[ROM] STOCK 4.3
<At&t Samsung Galaxy Note 3>
[OLD PHONES] At&t Galaxy Note 2, At&t Samsung Galaxy S2 Skyrocket, iPhone4s, iPhone 3gs <never again Nokia Brick, LG Flip Phone