Solid-state heat-capacity laser (SSHCL) has been developed in recent years. One of the key features of this heat capacity approach is the inversion of the temperature profile through the medium as compared to conditions where the laser is actively cooled while lasing takes place. So the thermal effects in the active medium on the two conditions mentioned above must be different. In this paper, we mostly discuss the contribution of temperature gradients to the effect of the thermal lens in optically pumped cylindrical laser rods operated in heat capacity operation through classical thermal conductivity equation, end effects and birefringence of the material with stress from temperature gradients ignored. Expressions are derived for the focus length of thermal lensing in laser rods for single-shot and repetitively pulsed operations. Programming the computer, we respectively calculate the thermal induced refractive power of the laser rods in the heat capacity operation and on the cooling condition, and compare the double results.