A method is proposed in the present study, by which the specific heat at constant pressure, cp, and the thermal expansion coefficient, αp, at different temperatures along an isobar can be derived from a single run of non-equilibrium molecular dynamics (NEMD) at using a steady temperature gradient. This study aims to demonstrate the method and examine its validity in the NEMD simulation. For Lennard-Jones fluids, it is shown that the cp and αp obtained from the NEMD simulations are in good agreement with those calculated in a traditional manner from the equilibrium fluctuations. The results of the present study suggest that a NEMD simulation with heat conduction is useful not only to measure thermal conductivity but also to determine these thermodynamic coefficients. In particular, there is a possibility that the present method is applicable even to heterogeneous systems, to which the standard method is difficult to apply.