My samsung galaxy note 3 battery suddenly runs out of power in mid afternoon. It used to only require recharging at night and last all day. No change in daytime usage habits. My phone is very warm on the back.
Have you added any new apps or perhaps one or two of your present apps have updated and their usage settings have change. This could be pulling your battery down. I would go into settings and see what is using power and then make some changes on what's using the battery.
A Warm or hot battery worries me. I have the Note 3 and rely on the phone a lot. Certainly look at what app is using a lot of battery power. If nothing seems new or unusual, then I would replace the battery. If the problem persists, then consider resetting your phone to factory.