while i dont have an answer to your problem I want to let you know you're not alone my Moto G also overheats it gets hot quickly unlike my other phones,
My Moto G is hot
I just got my Moto G today and ive used it for maybe 30 minutes doing basic things and its hot. Keep in my mind 1. Airplane Mode is on 2. I dont even have a SIM in the phone i use it as as a secondary device