Cubic crystals are often favored due to their interesting isotropic properties -such as the refractive index, the dilatation, etc-that simplify their use in laser systems. Among all Yb-doped high-symmetry materials, Yb:CaF2 is a very attractive one for high-energy high-power lasers. However, in such systems, thermal loads become important and thermal anisotropic effects can occur even for simple cubic crystals impacting severely the laser system design. In this context, we report here, a study of thermally induced polarization anisotropy in Yb-doped CaF2 laser crystals. Both thermal lens and thermally induced depolarization are precisely studied for different crystal orientations, namely the [110] and the [111] orientation. The study is performed with a pump/probe setup adapted to improve the signal-to-noise ratio under high power pumping. We observed both, classical-thermally induced depolarization and thermal lensing in accordance with previous work, but also, for certain configurations, atypical depolarization figures and astigmatic lenses. These results were also confronted with numerical simulations. The comparison between the [110] and the [111] oriented crystals represents a crucial study to determine the origins of these unusual effects and to allow a better understanding of thermal anisotropy in cubic laser-crystals.