The physical basis behind the simple hyperbolic heat transport model is discussed. The model equations are interpreted as energy equations for a system in a state of local nonequilibrium. On this basis a new boundary condition for the hyperbolic model is proposed when the temperature of a surface is given. It is based on a nonequilibrium situation and it reduces to the conventional boundary condition under the same assumptions as needed to justify Fourier's law of heat conduction and reduces to the known temperature-jump boundary condition at steady-state conditions. The significance of the new boundary condition is demonstrated through its application to one-dimensional heat transfer problems via hyperbolic equations. The difference between solutions of hyperbolic and Fourier models is found to be much larger than reported before and it does not vanish in the steady-state.