The required approach to investigate the electronic properties of spin-crossover (SCO) compounds needs to be able to provide a reliable estimate of high-spin/low-spin (HS/LS) energy gaps while retaining an accurate and efficient computation of the ground-state energy. We propose a reparametrization approach of the density functional theory (DFT) functionals to adjust the exact exchange admixture that governs the HS/LS energy splitting. Through the investigation of the thermodynamic properties of two typical SCO compounds, we demonstrate that the computed equilibrium temperature depends linearly, like the HS/LS energy gap, on the coefficient of the exact exchange admixture. We show that by taking the experimental value of the equilibrium temperature of the studied SCO compound as a reference, different hybrid functionals converge to comparable and realistic HS/LS energy gaps as well as enthalpy and entropy differences that agree well with the prior experimental investigations.