iPhone heats up and uses lots of data once a day I've got a new iPhone SE with all settings transferred from iPhone 5. 

I noticed that once a day, at around lunchtime, the phone heats up for around an hour or two, eats half of the battery and presumably also sends or receives a lot of data over 3G because every few days I get a SMS from my provider alerting me that I used 80% of my prepaid 1GB data. The phone is not on charger when this happens (I usually it recharge overnight).

This wasn't happening on the old iPhone 5 - there the 1GB of data lasted for a month or more and battery on light use easily for 2 days. 

I doubt it's the iCloud backup - it should only run over WiFi and while the phone is in charges (or so it says at least). I also have the background refresh turned off, email on manual fetch, firmware 9.3.3 (latest as of now), etc. All I could think of that could trigger some background activity was disabled. Yet still it happens every day.

What's going on here? Thanks!
Go into your cellular setting and start turning off apps that you don't want using cellular data. You might be able to narrow down which one is doing it. Also, make sure your hotspot setting is turned off.