Using a dynamical mathematical model, we investigated transient behavior of a water-water heat pump’s evaporator. The model consists of time and space dependent partial differential equations of water, pipe wall and refrigerant. Mathematically the thermal expansion valve (TEV) and compressor are described with lumped parameters and represent the boundary conditions. During the numerical solution of this system of equations the problem emerged of divergence of solutions. It was determined that the cause of the divergence solution was in the location of phase change of the refrigerant. The aim of this paper is, firstly, to display and propose a new approach to the elimination of divergence. In addition, it examines dynamic behavior of the heat pumps’ coaxial evaporator.