High power solid state lasers have wide applications; they have extensively attracted many attentions. When laser pumped, a lot of heat produces in it causes thermal effects such as stresses end effect and variations of refraction index. In this paper, we analytically study the thermal effects in an Nd: YAG solid state laser crystal which is pumped in longitude with a second order Gaussian (super Gaussian) profile. In this survey we neglect z derivatives of temperature distribution and also consider a statement in which thermal condition of cooler system is much more than thermal condition of laser crystal. Then we apply proper boundary conditions to probe thermal distribution function and related thermal effects. It will be shown that use of second order Gaussian profile for output beam of diode lasers is a better approximation for calculating the thermal distribution and estimating the thermal lensing than the Gaussian profile.