It shouldn't this phone is one of the best phones I know call the Company an tell them what's going on they will fix it, it a very Good phone take it from a person that has always has this prones.
Make sure you are using the new/correct cord. If they are hot too that may be the issue. I'd also try removing it from any protection case you have, if any. And, yes, go to a service office.
Get a replacement before the return time runs out. When I first got mine it did the same thing. But I kept doing the turn off and wait to cool. My return time expired. Then I had to follow all the steps recommended. Took about 2 weeks. Factory reset, Samsung support, ubreakitwefixit (which was 2 hour ride from my house and then wait 3 hours for them to work on. All they did was force updates. Got back home and over heated again. ) Report back to company after every step. They finally sent another phone but it was refurbished. I was totally upset because I paid so much to get a new phone, only to be given a used one. Plus having to reset and reload everything. Mine works great now. Just had to get past it being used. My daughter's worked great from day one.