iPhone 5S heating too much on using safari.
4. EDGE only, 3G very poor so EDGE only
5. WiFi always on at home
7. Powerful EDGE signal
One thing I have noticed is that in the absence of LTE and 3G signals, iPhones (and a lot of other smartphones, too) will expend a LOT of energy continually searching for one of these signals, even if a good EDGE signal is available. I've noticed my iPhone 5 and 5s both got VERY hot when no LTE signal is available and battery life would really go downhill, even if a decent "4G" signal were available and already connected.
Have you gone into settings and manually turned LTE off? If not, then I would suggest doing so. This will force the phone to stop searching for an LTE signal that isn't there. This should help cool it down a bit.
If you're still having trouble, you might need to shut off cellular data altogether while connected to your home WiFi. You'll still be able to get calls and SMS messages. All data will just have to go through the WiFi connection. Of course you'll have to remember to turn cell data back on when you're out of range of any WiFi.
