I had this happen occasionally with various beta versions of iOS 11 and 11.1 on my iPhone 5s. With some of these updates, it seemed like - only for a day or two - higher battery drain and an occasional random restart. Such random restarts that I noticed amounted to no more than once or twice within one or two days of such iOS "update"/installation, all O.T.A., for at least a few such iOS beta versions. There were probably a few more random restarts that I didn't notice. Everything would eventually settle down a day or two after each one of these iOS O.T.A. updates.
I've read postings online that speculate that it has something to do with heavy-duty iOS Spotlight re-indexing that goes on for a while after installing this or that version of iOS 11.
You can view event analytics via Settings > Privacy > Analytics > Analytics Data > (Data.) It's all Greek to me.
You can presumably help Apple fix such problems by sharing your analytics with them via
Settings > Privacy > Analytics > Share iPhone Analytics: enable.
I got off the beta track when the official public release of iOS 11.1 came out and am running that (installed via iTunes, not O.T.A.) and it's the calmest and coolest my 5s has been in a few months so I'm going to keep it right there and forget about 11.1.1, at least for a while, as my 5s has never had the character display bug.
I thought it might have something to do with the 5s having only 1 GB of RAM but the SE has 2.
I thought it might have something to do with APFS but that came out with iOS 10 and I don't recall noticing any random restarts prior to iOS 11.
I thought it might have something to with analytics sharing (with Apple.) I let it all hang out. Whenever I noticed a random restart, I'd think maybe that's associated with a huge analytic data upload to Apple especially since it was with beta iOS, 11 & 11.1 being the only iOS versions of which I've run beta versions.