Heat conduction in a medium can be modelled as the motion of a weighty phonon gas in a dielectric based on the concept of thermomass. Newtonian mechanics has then been used to establish the momentum equation for the phonon gas, which is the general conduction law and it degenerates into various heat conduction models for the appropriate simplified conditions. These phenomena show that heat has energymass duality, that is, heat acts like energy during its conversion with other forms of energy and then acts like mass during its motion. Furthermore, the general relation between the heat flux and the temperature gradient can be derived from the Boltzmann transport equation for phonons. In the high heat flux case the thermal conductivity for nano-materials calculated based on Fourier’s law is the apparent thermal conductivity, which is less than the actual intrinsic thermal conductivity. A more general heat conduction model for nano-systems is then presented. Finally, the quantity, entransy, is introduced based on an analogy between heat conduction and electric conduction, which is a simplified expression of the thermomass potential energy. The principle of minimum entransy dissipation-based thermal resistance can be used for optimizing the heat transfer process to increase the energy efficiency.