A free jet of high Prandtl number fluid impinging perpendicularly on a solid substrate of finite thickness containing small discrete heat sources on the opposite surface has been analyzed. Both solid and fluid regions have been modeled and solved as a conjugate problem. Equations for the conservation of mass, momentum, and energy were solved taking into account the transport processes at the solid–liquid and liquid–gas interfaces. The shape and location of the free surface (liquid–gas interface) was determined iteratively as a part of the solution process by satisfying the kinematic condition as well as the balance of normal and shear forces at this interface. The number of elements in the fluid and solid regions were determined from a systematic grid-independence study. A non-uniform grid distribution was used to adequately capture large variations near the solid–fluid interface. Computed results included velocity, temperature, and pressure distributions in the fluid, and the local and average heat transfer coefficients at the solid–fluid interface. Computations were carried out to investigate the influence of different operating parameters such as jet velocity, heat flux, plate thickness, and plate material. Numerical results were validated with available experimental data. It was found that the local heat transfer coefficient is maximum at the center of the disk and decreases gradually with radius as the flow moves downstream. The thickness of the disk as well as the location of discrete sources showed strong influence on the maximum temperature and the average heat transfer coefficient.