Thermally induced optical distortions severely degrade the quality of a laser beam, thus reducing the irradiance on the target. Procedures are formulated to evaluate the impact of spherical aberrations generated by actively cooled cylindrical components that transmit cw laser radiation. Specifically, we deal with edge- and face-cooled optical elements and examine how beam shape and cooling strength affect the performance. The heat-flow equation is formulated nondimensionally and solved analytically, thus demonstrating that (1) temperature gradients causing optical distortion scale with ?PIK, i.e., the power deposited per unit length and the thermal resistivity of the medium; (2) in most instances, fourth-order polynomials yield reasonably accurate temperature profiles; and (3) apodization can be very useful in mitigating the deleterious effects of thermal lensing. For edge-cooled components, the heat-transfer coefficient has no influence on the temperature profile, and the diameter does not affect the performance. The treatment of face cooling requires a more elaborate analysis; for weak cooling, the spherical aberration factors are similar to those associated with edge cooling, but Biot numbers ?10 are required to achieve a significant reduction of the distortion.