We present a new computational method developed for fluid flows, in which both compressibility and thermal expansion effects are important. Application of the method in transient thermal-hydraulic analysis of nuclear steam generators is also presented. The fluid model is based on one-dimensional, nonlinear, single-fluid conservation equations for mass, momentum, and energy. An empirical slip flow model is included to enable description of two-phase flows as well as single-phase flows. Numerical solution is based on the implicit continuous-fluid Eulerian (ICE) method, which provides stable numerical solutions for compressible fluid flows. An extension of this method (designated as the EICE method) is developed to account for thermal expansion effects. This is achieved by including implicit energy dependence in coupled equations of mass, momentum, and state, and solving the full system of fluid equations through a two-step iterative technique. The development of the EICE method is presented and discussed, along with specific calculations for once-through and U-tube steam generator transients, natural flow oscillations, and a vessel blowdown transient.