There are no models in scientific literature that satisfyingly simulate the behaviour of real Stirling engines, once that performance prediction models estimate errors above 7%, a barrier to be broken in new engine projects. This work presents a methodology that aims not only to reduce the error in the prediction of the indicated power in beta-type Stirling engines, but also to facilitate extrapolation without the necessity of experimental data. For that, strategies are combined to calculate initial and boundary conditions which are used on a transient simulation in computational fluid dynamics. The first-order model of Schmidt allows to calculate the pressure inside the engine exactly when the power piston is on the bottom dead centre with an average error of 21.3%. The temperature on displacer piston faces can be acquired through a steady-state simulation in CFD (without piston movement). In this methodology, the pressure and the temperature profile are respectively used as initial and boundary conditions for a transient simulation in ANSYS(center dot) Fluent, reducing the stabilisation time. The inclusion of the Discrete Ordinates radiation model increases the displacer's frontal face temperature by 132.2 K and results in an indicated power prediction improvement with an error reduction from -14.4% to -2.6% when compared to experimental values. In this way, the presented methodology consists in the combination of first-order mathematical models with CFD simulations, which enables extrapolation for other conditions in beta-type Stirling engines without the necessity of initial and boundary experimental conditions, obtaining an error around -2.6% (2.70 W for experimental and 2.63 W for simulation). Thus, with this methodology, it is possible to design a new project of beta-type Stirling engines through laboratory prototypes enhancing the power accurately.