Answer: Afther long time, the average energies of the particles of both objects will be the same
Explanation: The temperature of an object is related to the kinetic energy of the particles that form it.
This means that the hot object has particles with more kinetic energy than the cool object.
Now, if we let them interact ( the interaction here is the conduction) the hot object will transfer thermal energy to the other object, in this way reducing its own particle's kinetic energy and increasing the kinetic energy in the other (cooler) object.
As time passes, the system will reach the equilibrium, this means that both objects will have the same temperature. At this point, the average kinetic energies of the particles in both objects will be the same (because the temperatures are equal)