The hypermagnetizability and the hypermagnetizability anisotropy of CO2, N2O, OCS, and CS2 are computed at a wavelength of 632.8 nm using cubic response theory with multiconfigurational self-consistent field wave functions. The anisotropies of the electric dipole polarizability and of the magnetizability are also obtained. This allows us to study the temperature dependence of the Cotton-Mouton constant for all four molecules and thus to compare to the results of the experimental study by Kling and Huttner [Chem. Phys. Lett. 90, 207 (1984)]. We also assess the importance of pure and zero-point vibrational effects on the relevant molecular properties. In particular, we show that for CO2, OCS, and CS2, the pure vibrational effects to the hypermagnetizability anisotropy can be even more important than the electronic contribution.