iPhone 5 getting very hot while using 3G

I purchased an unlocked iPhone 5 in the UK and brought it with me to Greece. The first company I got a pay as you go nano-sim from didn't offer much internet so I never had it turned on and my phone would stay cool, while lasting 2 days with 8 hours of use on a full charge.

Today, I acquired a new provider with better internet in my area. They didn't give me a nano-sim but instead cut a normal sim down to size. I noticed the silicon was a little scratched at the edge.

When I used 3G, even in the city centre, the phone heats up a lot and the battery percentage drains very rapidly which kind of sucks.

Is this normal for all iPhone 5s or is there something amiss (ie either not a strong signal or perhaps the damaged sim)?

Would be nice to hear other's views!

Well, I thought it was implied in my post that I was doing nothing different other than using 3G internet to browse. I was using the Facebook app and the iOS browser.

Did I really need to specify that? I mean, it's not as if I had suddenly engaged in heavy rendering on my phone immediately after acquiring 3G... That's "literally" the only difference; without 3g internet enabled > phone cold/battery last long time. With 3g internet enabled > phone hot/battery no last long time.

There are no other variables.