The unsteady conjugated heat transfer between a finite thick plate and an incompressible laminar flow started impulsively at its leading edge is investigated analytically. The unsteady fluid-energy equation and the 2D unsteady plate-conduction equation are derived, solved by the successive approximation technique of Shvets (1951) and the Fourier-series method, respectively, and coupled via the boundary conditions of heat flux and temperature at the fluid/solid interface. The numerical results are presented graphically, and transient, intermediate, and steady-state regions are characterized. The model is shown to give good predictions of the transient Nusselt number, the thicknesses of the hydrodynamic and thermal boundary layers, and the response of fluid and wall temperature to step changes in the velocity and temperature of the incoming fluid.