If two bodies have same temperature but the amount of heat energy in both of them is different. Will there be a flow of heat energy between them if both bodies are placed in contact and will the temperature rise in any of the bodies? 

As the temperature of the two bodies are same they are in thermal equilibrium which means there would be no transfer of heat energy between them.Flow of heat energy takes place when there is temperature difference between the bodies which are in contact with each other.