Why is my iPhone 5S overheating so much?

Activities such as:

1. Phone Calls that last around 10 minutes


2. 3G Browsing for 5 - 7 minutes


3. Watching videos for 5 minutes


4. Using apps such as facebook / instagram etc for 5 - 7 minutes, lead to my iPhone 5S severely overheating.

It heats so much at times that it can't be held any more and you have to set it down for it to cool down.

At times, it randomly restarts when plugged in. When it starts to heat the battery drops sharply and sometimes the phone simply dies

I'm fairly certain that the hardware in my phone is being affected with this overheating

My first year phone warranty ends in 10 days and I'm contemplating whether I should give it to Apple India Service and if they will replace my phone.

Any Solutions? Suggestions? Experiences with Indian Apple Service Centres?