whenever a phone is charging it heat up. this is a result of the current flowing into the phone. heat is the most basic form of energy so all energy produces heat as a byproduct. if the phone is very hot then it will stop charging. One solution to keep your phone from getting too hot is to get a charger with a lower current, under 1 amp of charge so that it will not heat up so much. charge the phone while it is off also just to keep it as cool as possible. Make sure that the battery is actually fitting inside the slot and connect properly. it will take a while for the phone to have enough charge to turn on since it is getting a trickle charge. Just try leaving it on the charger for at least an hour maybe more. I hope that this is helpful and that you get your phone to come back on.
if it is not the charger then also try this, while off the charger hold down the power button for 30 seconds then release it. also try the hold down the power button for 30 seconds while on the charger. sometimes the phones need a reset to come on and charge correctly. once again i hope that this is helpful.