Using the anisotropic thermal expansion coefficients and the negative refractive index gradients in temperature of an optical-pumped Yb³⁺∶KGd(WO₄)₂, it is possible to find some special directions without thermallyinduced lens effects which is called“the thermal-lens-free orientation”. Considering there are some defects in the theoretical models created by other researchers, the thermal expansion tensors and thermal-lens-free orientations at different polarized directions have been evaluated by using the least square method and two-order tensor rotation approach. The thermal-lens-free orientations have been determined as follows: The directions located ±46.3° from the p axis in the p-g plane when the light is polarized in the m axis, the directions located 24.9° clockwise from the m axis in the m-g plane and 81.2° counterclockwise from the m axis in the m-g plane when the light is polarized in the p direction. When the light is polarized along the g direction, there is no thermal-lens-free direction for the crystal. The theoretical results in the previous reports are compared and some defects are also pointed out. The optical path changes have been analyzed along the directions of both 17° rotated clockwise from the m axis in the m-g plane (p-polarized) and the b axis (m-polarized) to compare with the previous experimental results. The effectiveness of our theoretical simulation has been therefore demonstrated through the comparison analyses.