Powering 36V motor with 48V LiPo battery through a motor controller
As from all the comments, I see that running the motor with a higher rating battery will result in killing it at some point. Thus, I ended up buying a 36v battery, however, it was a 6 hours one-way drive to get to the nearest shop that sells them and it was the last piece. 

I don't consider this as a real answer though. I am looking forward to find someone who managed to do it and share his experience on how he managed it. But, the Science says the motor will die.