sorry for the long delay, I have L1320 LTE, I know that it suffers overheating, seen some people online with the same phone complain about the same issue
but that overheating doesn't make sense and shouldn't exist unless something was causing it, I 'm sure that the hardware of my phone isn't faulty, some when during the middle of this year I asked Gabe Aul on his twitter account about what may cause a phone to overheat so much that it turns off to protect itself, he told me that there's a background process to blame, couldn't think about anything running in the back ground except the location services (and probably syncing features but these aren't CPU Intensive, so the location service is what to take the blame
I used both 8.1 and 10, they both make the phone overheat (10 does more), 8.1 seems to do while using Cortana or search, using my cellular data (3G) also does an overheating job (not really on 8.1, but dangerously on 10, overheats so much when being used and warm when IDLE with data ON)
I noticed that whatsapp plays a big role in overheating too (overheating intensifies on both 10 and 8.1 (more on 10)), I remember facing overheating issues (and turning off) while using FB and FB messenger (I no longer use them since I closed my FB account)
there really IS something going in the background