there was no original charger provided with the moto g. I know that some stores sold the moto g with an additional charger but it they did it themselfs.
it is pretty normal that phones get hot while charging, because of the chemical reaction in the battery. If the phone is in use while charging it gets even hotter. When I charge the moto g in the car, while using maps on it, the battery reaches temperatures of around 45 °C, which is not good, but still acceptable for the circumstances.
In germany there was a recall because one company added a charger that could break the charging port. the charger was from the company "iProtect". I was affected by this and could easily exchange it, the store just sent me an original motorola charger that charged a little slower (around 850 ma compared to 1a of the first charger).
If you want your phone to get less hot while charging you can do the following:
1. don't charge it at a hot place (like on a window ledge where the sun is shining, in the sauna or near a heater)
2. don't use your phone while charging (the CPU and GPU also create heat when they get stressed)
3. use a charger with a lower ampere rating (the moto G support all chargers that output 5v and 0.5 - 1.5 a. I have a charger from a sony headset (MW600) that only outputs around 600 ma that I use when charging over night. in day to day situations I use the 850 ma charger from motorola and if I'm in a hurry I use the 1a charger from my HTC.