Iphone 5S over heated and stopped working

The iphone was switched on but not in use, the phone become very hot and the battery drained completely. I cooled the phone and connected to power for charging the bayyery, but the iphone has stoped working as it only comes up with lunites apple symbol on the screen. SInece than I tried restoring the iphone via itunes, but comes up with erro 21 just after it has decompressed the down load. I also notice that the serial number is set to NA on the itune screen. Any help would be very much appreaciated.

thank you