Laser heating offers considerable advantages over conventional methods. The closed-form solution for the temperature rise in the substrate during the laser heating process gives insight into the physical phenomena involving during the heating process and the material response to a laser heating pulse. In the present study, the exact solution for the temperature rise due to a time exponentially varying pulse and convective boundary condition at the surface is obtained. The closed-form solution to the solutions available in the literature for a step input intensity pulse with a convective boundary condition at the surface as well as a time exponentially varying pulse with a non-convective boundary condition at the surface is deduced. A Laplace transformation method is used in the analysis. In order to account for a pulse resembling a typical laser pulse, an intensity function resulting in exponentially increasing and decaying intensity distribution is employed in the source term in the governing transport equation. The effects of the pulse parameters beta', beta'/gamma' and Blot number Bi on the resulting temperature profiles are presented and the material response to a pulse profile resembling a typical actual laser pulse is discussed. It is found that the closed-form solution obtained in the present study becomes identical with those presented in the previous studies for different pulse and boundary conditions. Moreover, the coupling effect of pulse parameter beta' and Bi is significant for the temperature rise at the surface.