This paper treats transient cooling of a hot solid by an impinging circular free surface liquid jet. The flow and thermal fields in the liquid as well as the temperature distributions in the hot solid have been predicted numerically. The Navier-Stokes equations for incompressible fluid flow in an axisymmetric coordinate system and the transient heat conduction equation for a solid Rave been solved by a finite difference method. The hydrodynamics of the liquid film and the heat transfer processes have been investigated to understand the physics of the phenomena.