In this paper

based on the analysis of the heating and cooling mechanisms within an edge-cooled and end pumped laser rod

we simplify the heat transfer equation in an axisymmetric system into a one-dimension one

taking into account only the radial heat flow.As an application

we solve the simplified equation to derive the expressions of the temperature distribution in two practical cases

that is

in laser rods end-pumped by a Gaussian beam or a top-hat beam

respectively.The results tell that a pump source with intensity of Gaussian shape causes to a higher temperature rise and a more severe nonuniform temperature distribution within the rod than that caused by a top-hat source with a pump radius the same as the former.The discussion is cast into a nondimensional form so that the results can be applied to various materials.