Firstly, android OS using 80% when you aren't doing anything isn't necessarily a problem at all. Remember that's a percentage of the power that has been used, not an absolute power drain. So if you are using very little power but nothing else is running then the OS will use a large percentage of the very little power that is being used, and that's fine.
You don't say how hot, but running these high-powered chips hard will generate a lot of heat, so phones heating up during gaming is common. The chip should throttle if it thinks it's getting too hot (limits clock speed) - if you see the game become choppy when it heats up that's what's happening. Wait and see what Note 3 owners have to say, or post the actual temperatures (and what games you are playing) if you want to give more information, but while I don't own a Note 3 so can't talk from experience of that handset what you describe doesn't sound too unusual to me.
The biggest threat from heat is to battery longevity. As the N3 has a removable battery that may not worry you so much, but I'd not recommend gaming while the phone is charging.