I had this problem for the first time with my original iPhone 7, which I bought on launch day and which had appropriate battery life until late February (prior to iOS 10.3). At that time, the battery began to drain very quickly even when the phone was not being used, usage and standby times were reported as the same when they were not, and the phone became excessively hot. Apple support had me do all the usual trouble-shooting, then had me take the phone to the Apple Store, where they had me set it up as a new phone to see if that solved the problem.
It worked OK for about two days, then the problems began again. So they gave me a replacement phone which they also made me set up as a new phone. As anyone who has done it knows, setting an iPhone up as a new phone is a lot more time-consuming than restoring from a backup, but I understand that they wanted to avoid carrying over any corrupt files from my backup.
From March 8 until April 25, my first replacement phone worked well, but then it began with the same problems, rapid battery drain even when the phone was just sitting being unused, usage and standby time reported as the same, and over-heating. Apple support did remote diagnostics which indicated some sort of problem with the phone, so they had me take it in for a second replacement phone. Again, I had to set this up as a new phone. By now, I had spent many hours either with support or setting up my iPhone.
The second replacement phone lasted until early May, when it began to show the same problems. One time, it drained from 90% to 0% (dead) overnight. Apple support, reviewing my history, told me just to take it in and get another one, which I did. On May 5, I received my third replacement phone, which I again set up as a new phone.
That one lasted from May 5 until May 19, when it again started draining rapidly, heating up, and reporting incorrect times for standby and usage. I even took screen shots this time, which showed that at one point, the phone was draining 1% a minute, and I had taken a screen shot to show that no apps were open. The screenshots also showed that the phone had drained from 94% to 13% in less than 5 hours, sitting idle and not being used.
I called Apple support again, was walked through all the usual trouble-shooting steps, and received suggestions such as "turn off bluetooth when you're not using it" (impossible, I have an Apple Watch), turn off *all* background activity (I had already turned it off except for apps which require it in order to work), and other suggestions from the usual "battery saving" tips. The fact remains that the worst battery drain with all the iPhone 7 units I have had occurred when the phone was *not being used* (I had long ago gotten into the habit of closing out of all apps before leaving the phone idle for any amount of time, which should not be necessary).
The tech support guy yesterday connected me to a senior advisor, who seemed to realize that this was getting absurd, and he told me to return the phone one more time and hopefully the fourth replacement phone would work properly. He said that there was no need to set this one up as a new phone since that had not seemed to make any difference with the previous phones, so at least it only took me a couple hours to get my phone restored, re-download music and other data that is not saved in a backup, and synched with my Apple Watch.
The senior advisor also told me that if the fourth replacement phone, my fifth iPhone 7 (counting the one I bought new on launch day) does not work out, they will give me a new "white box" phone. I have been asking all along what the difference is between a replacement phone and a new phone, and have received different answers, ranging from "they are exactly the same except for the box" to "the replacement phones are re-manufactured phones that use new parts for all the components you see, such as the body and the screen, but may contain previously used components on the inside". When I asked if that could include a used battery, I was told that it could, but that the battery would have to pass a test before it would be used.
The senior advisor also told me that Apple will *only* issue a "white box" phone if a customer has been given four replacement phones that have not worked. That seems like a rather high number of replacement phones to have to go through, especially when you start to count up the hours you spend with Apple support (typically a couple hours for each phone), in the Apple Store (another hour or so), and then setting up the phone as new or restoring it (which can be several hours or more).
Aside from my original iPhone, which I purchased new and which was using iOS 10.2.1 when it started having battery problems, all the other phones have been using the latest version of iOS 10.3.
The fourth replacement seems to be working fine so far, but they have *all* worked fine for the first few weeks. The last one worked fine until the day before it started over-heating and draining quickly.
I've become skeptical about the replacement phones. I am *not* opposed to the idea of replacement products: I have received replacement iPhones in the past and they have worked out fine; I've had a replacement iPad and a replacement Apple Watch, and again, no problems. But either I have had incredibly bad luck with the iPhone 7, or it's a problem with iOS 10.3, or the quality control of the replacement iPhone 7's isn't what it should be. I have no idea what's going on, but it's annoying and time-consuming and I just want a phone that will work reliably.
I am posting this because the battery issues that have been reported by others in this thread are not normal, and while you may be able to fix them by using the standard troubleshooting and battery-saving tips, don't give up if that does not work. Contact Apple and let them know what is going on. I cannot say that my problem has been resolved yet, but at least this time, I feel that there is an acceptable plan in place in case this iPhone, my fifth one, fails.