A numerical and experimental study is conducted to investigate the effects of heat transfer on the squeeze-film flow between two parallel rotating disks, one of which is flat while the other has a grooved, highly rough surface. A conjugate heat transfer technique is developed to evaluate the torque and temperature distribution within the thin-film lubrication system, as the two disks advance toward each other. For the fluid domain, the energy equation is solved simultaneously with the squeeze-film equations coupled with an empirical contact model. Additionally, the energy equation is solved for the flat disk to determine the heat transfer by conduction while the grooved disk is assumed to be adiabatic. The heat exchange at the solid-fluid interface is determined iteratively using the energy equations from both the fluid and solid domains. The governing equations are solved using the finite volume method, and the numerical model is tested for grid convergence and conservation of energy. An experimental study is conducted to collect torque and temperature data that are used to validate the model for the engagement dynamics of a wet clutch. The numerical and experimental analyses demonstrate the importance of thermal effects when evaluating the dynamics of squeeze-film flow between two rotating disks. Heat transfer affects the viscous and mixed lubrication phases of the engagement process significantly, especially for low initial temperatures. Moreover, the study highlights the strong effects of flow recirculation on heat transfer due to the complex geometry of the grooved friction material.