I just got a 5S the other day (upgraded from a 4s). I have EVERY option turned on that can be... icloud, I have 6 email accounts, 3 icloud, 3 non and the phone checks the non apple emails every 15 mins.
My 5s has a mophie case on it so the phone thinks it's on AC (technically DC). That way it never drops Wifi when locked.
I never gets hot.. even when gaming.. warm, but not hot
A hot phone is usually cause by a few things
1a) Massive use (brightness cranked to max, and playing a CPU/GPU intensive game). This wil get a phone or ipad fairly warm...
1b) MASSIVE use of CPU due to a service or services that have corrupted settings going crazy on the device.
2) do 1A above while on DC power and the phone or device can get REALLY hot, and even activate thermal shutdown - especially if you use Apple's new 12W charger. Charging the battery generates heat. So high use plus charging will heat things (even if the charger isn't strong enough and the battery slowly drains, it will heat up). I use a Y device that lets me use a second charger, and I inject a 5V, 5Amp power source. This lets an ipad 3,4,or 5 be under HEAVY use and not drain the battery..but the device can get hot. It's safe as each device has a limit of how many volts/amps it will draw
3) This one is a no brainer .. don't leave the device in direct sunlight or warn room temps over 80-85F under heavy load.
The phone shouldn't get hot like the OP's phone with such little use. It sounds like there was an icloud issue, and it was solved. However if ANY ios device does this after a full erase and set up NEW (no restore), then it's probably a hardware fault. (if it were an ios bug, the all devices would have the heat issue).
ios does NOT constantly use icloud... I should say it SHOULDNT... It ONLY sends docs and data (if turned on) ONLY when you USE the app and save the data... OR every 24-36 hrs, it backs the phone up to icloud (if turned on AND you are on Wifi, AND it's running off power and not battery). Once you get past the initial FULL backup, the device uses incremental backups that should finish in 1-5 mins depending on your wifi / internet speed (and how many pictures, documents an app data you have). Eventually icloud will delete the backup and do a full backup and resume incremental backups (this safety thing in case your "base" backup gets corrupted on the apple servers ... and YES.. that has happened)
The OP's situation is usually caused by iphone upgrades. The settings from one phone gen to the next don't always restore properly (even if it's the same ios version).
icloud also doesn't backup all your passwords, and app data
TBH, icloud backup should be used, but only as an "oops" in case your itunes backup has an issue. The best way to backup and restore ios devices is with an encrypted itunes back up
1) an encrypted back up saves any and ALL passwords and secure features of the device (icloud backups do not fully support this)
2) backing up and restoring from itunes is a LOT faster. USB 2.0 is 480Mbits/sec (60 MegaBytes/sec). Granted NO ios device can handle moving data at those speeds plus there's overhead to consider. About 50MB/sec is as fast as you can go (a SATA 3 HDD or SSD can EASILY hit that cap) Even the most up to date devices can only move about 15-20MB/sec of data. Hence why no ios device is usb 3.0... No point. The read/write speed of the storage is just too slow.
That's still a LOT faster than any internet connection most people will use 🙂
I have a 110Mbit/20Mbit Time Warner Business class cable modem connection in my house (you don't want to know what I pay for that LOL). Even at my speeds, I can only pull 13.75MB (megabytes/sec).. and that's providing a site supports that.. Apple does NOT...Apple caps all app, music, movies, tv. blah blah at 35MB/sec for any of their services. I have a 64GB iphone 5s. Restoring and backing it up goes FAST as my 5S is mostly all music with some apps. My 128GB ipad 5 has 64GB of apps, no music (set to iTunes match as my phone plays my tunes).. and the other 64GB are video. I would NOT want to restore my ipad and have to DL 64GB of apps!! Not at apple's speed caps!
So as you can see, backup/restore from itunes a LOT safer, and less buggy
When I backed up my 4S to icloud and restored it to my new 5s, it prompted me for SOMEONE ELSES Apple ID! Apple thought it was the new activation lock feature, and that I got sold a used phone.. not the case.. the icloud servers accidentally tossed a few apps linked to another person's apple ID into MY backup. Deleting the icloud backup, backing up my 4S again, and restoring to the 5S solved it. I wasn't at home which is why I didn't use my itunes.