The heat transfer that we'll have will be:
- At first, the metal bar will emanate heat through radiation, to the atmosphere, and to the second metal, through conduction.
- Because of this, the second bar will start to increase it's temperature, up to the fusion point, spending the energy received on the fusion, and also radiating heat to the atmosphere. It won't emit heat in any other form, since heat transmission can happen only from a hot body to a cooler one, and the only things in contact are the two bars.