Heat of fusion is a property of a material telling us how much energy it will have to gain or release (per gram) to change state between being a liquid and being a solid. It has nothing to do with the exchange of energy between two materials when neither changes state, so we can eliminate choice 1 here. Much the same can be said for choice 3, different melting points. Since there is no change of state in the scenario, this is not a factor. It is worth noting that the energy required to change state is often quite different from the energy required to simply change temperature for a given substance.
Specific heat tells us how much energy must be absorbed by a substance (again, usually calculated per gram of material) to change temperature by one degree. While this is relevant to the question, two blocks of metal with the same specific heat could still exchange energy, providing they were at different temperatures to begin with. This means that the correct answer to your question is choice 2, different initial temperatures.