Note 7 is so awesome, I love/d it. For me I never had problems of hot battery, not on first gen, nor on second gen. Im not a gamer tho. Highest i went to was 34c.
Obviously i cannot recommend N7, one is due to recall (which is bogus) and two is because most are deactivated via IMEI + some other sh1t. My 1st gen is still working on rogers tho and my gf having a "blast" lol
Kinda envy her. So for now im playing with my N7 on wifi and for everything else using LG G3 which i like but it does feel light years behind.
If you love the stylist phone then you have no choice but to wait for N8, unless we could figure out how to unblock N7 but for now most are unsuccessful, specially Canadian versions.
From what i've heard S8 should be great, so there is another good choice for you and by that time Im sure LG G6 is going to come out as well which looks good design wise. Not sure how it will stack up vs S8.
The Note 7 pretty much has it all. All great sammy tweaks like always on display, button camera lunch - S.Pen, Curved screen, Best quality display, water proof, almost no bezels, usb type C, FAST wireless charging. Type C i never used since i had wireless everywhere, even my cars but now with this LG G3 I sure wish I had it. Feels like Ill break the damn thing off lol.
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Ps If I was in your shoes Id keep whatever you have now, struggle with it and wait for S8, N8. Worth the wait.