This work applies an effective and efficient method, called Numerical Simulation-Aided Parametric Analysis (NSAPA), to derive simple and accurate correlation formulae for a natural convective flow system. The classical natural convection in roofs of triangular enclosures is considered to demonstrate the effectiveness of the approach. The buoyancy force generated by the temperature gradient generates a flow pattern. The NSAPA technique derives a set of algebraic equations in characteristic quantities from mass, momentum, and energy conservative equations for natural convection inside a triangular enclosure. The main advantage of the NSAPA technique is that solving the set of algebraic equations is easier than solving the original system of partial differential equations using a numerical method used in computational fluid dynamics. The heat transfer coefficients can be derived using these characteristic quantities. The numerical solution determines the constant factors of the characteristic velocities, the characteristic temperature, and the heat transfer coefficient. Comparisons of these results obtained using NSAPA with the direct numerical solutions demonstrate the excellent performance of the proposed method. Finally, the heat transfer coefficients in the equations that apply to roofs of triangular enclosures are considered in relation to a particular range of related parameters. The contributions of the NSAPA technique in this study are that little effort is required to implement the NSAPA procedure, the dependence of the thermal flow characteristics in the roof of the triangular enclosure on the parameters is clear, and these simple linear empirical equations are useful to energy management designers in the consideration of the flow field of a housetop.