Liquid-cooled servers can be deployed to reduce the energy consumption and environmental footprint of hybrid-cooled data centers. A computational fluid dynamics (CFD) model can bring extremely useful insights and results for thermal simulations of air- and liquid-cooled servers in a single environment. In this study, a conjugate heat transfer (CHT) numerical model is developed and validated with experimental data to simulate heat transfer from the CPU to the air and cold plate considering the effect of thermal paste. The cooling performance of an in-house developed cold plate design is thoroughly investigated via the validated CHT model. A dataset containing one hundred samples of various flow, thermal and workload conditions was generated using the Latin hypercube sampling (LHS) method, which was further utilized in the series of CHT simulations. Finally, a novel empirical equation is proposed for the prediction of heat transfer from the CPU to the air. The accuracy of the proposed equation is confirmed by comparing estimated and simulated results for a test dataset. A thermal analysis of a rack containing air and liquid-cooled servers is performed using the presented approach. The simulation results reveal that the proposed compact model can be used reliably for the thermal simulation of a hybrid-cooled data center.