A new quasi-one-dimensional procedure (one-dimensional with area change) is presented for the transient solution of real-fluid flows in lines and volumes including heat transfer effects. The solver will be integrated into a larger suite of software modules developed for simulating rocket engines and propulsion systems. The solution procedure is coupled with a state-of-the-art real-fluid property database so that both compressible and incompressible fluids may be considered using the same procedure. The numerical techniques used in this procedure are described. Test cases modeling transient flow of nitrogen, water, and hydrogen are presented to demonstrate the capability of the current technique.