My battery life with ios7 has improved a lot over the course of a few days. Definitely turn off auto-updating of apps in the background. To do so, go to Settings > iTunes and Apple Store, and disable the Updates option. Just don't forget to check the App Store for new app versions. I think that so many app updates came out over the last week that every time the phone was awake, it was refreshing these. I also think that maybe spotlight was reindexing and it's done with most of it's work and that there were other processes that had to update similarly. That would explain the overheating etc even when you think you are doing nothing.
Right now, my phone is at 75%. It has been unplugged from charging for 2.5 hours. The other day, that would have been after 30 minutes uncharged. It has been running apps requiring wifi the entire time, at first I was doing my regular email checks and random searches (about 30 minutes straight) and also a few updates from the App store. Very internet intensive. Since then, it has been running itunes Radio for 2 hours straight to airplay speakers in my house. I normally plug it in to charger while doing that. I think that is pretty good because Apple only gives the iphone 4s up to 9 hours of wifi internet use. At my rate of use, the 4s will last 10 hours, albeit mostly with the screen off. That does seem on track.
(BTW, although I am not thrilled with the battery usage, I love some of the new features of ios 7 and I would not downgrade and give those up. iTunes radio is great, although I used iheartRadio for that feature in the past. What really works well is email, particularly searching for old emails across multiple accounts. It is very fast and accurate IMO. The old ios would often not find messages that came up on my computer. It was frustrating and unreliable.)