F7 F8 & F9 keys melted on brand new MacBook Pro (2015) with Retina Display. Why?

Maybe a short circuit? Take it to an authorized service place for assessment as I presume it is still under warranty.

How to find your nearest Apple Authorized Service Provider (AASP) or Apple Authorized Distributor (AAD) - http://support.apple.com/kb/HT1434

Genius reservation http://www.apple.com/retail/geniusbar/

on-line https://getsupport.apple.com/GetproductgroupList.action

check warranty https://selfsolve.apple.com/agreementWarrantyDynamic.do