A numerical model of the rod laser medium pumped by laser-diode array (LDA) end is set up. Considering the influence of temperature correlation of the thermodynamic parameters of the material and heat transfer coefficient between air and medium, using the thermal conduction equations and the thermal-elastic equations, the transient distributions of temperature and thermal stress and strain in the composite rod medium and un-composite rod medium are calculated by the finite element analysis method. The effects of pump power and heat transfer coefficient and time on transient distributions of temperature and thermal stress and strain in the medium are analyzed. The results indicate that the positions of maximal temperature maximal tensile stress and maximal axial strain of the composite rod are different from those of the un-composite rod. And the maximal temperature, maximal tensile stress and maximal axial strain of the composite rod are respectively 73 per cent, 60 per cemt, and 33 per cent of the corresponding values of the un-composite rod. It is obvious that the thermal effect of the composite rod is greatly reduced. The theoretical results provide theoretical reference for the design of solid laser pumped by LDA and experimental study.