According to the Kinetic Molecular Theory, the temperature of a sample is the average kinetic energy of particles in a substance.
This also expains the relationship between the temperature and the states of matter. Molecules in a solid are held close to each other, being able to vibrate but staying in place. If the molecules are able to move more freely, the sample is a liquid or a gas.
Since both bars have a temperature below their melting point, they are both solid. One bar has a greater temperature: 80ºC, while the other bar has a temperature of 20ºC. Since the temperature is related to the average kinetic energy of the sample, then the molecules in the 80ºC have a greater average kinetic energy.
Then, the statement I is incorrect because both bars are solid, so their molecules move around equally freely. The statements II and III are correct.
Therefore, the correct choice is: II and III.