1) Background: the modeling, characterization, transformation and propagation of high-power CW laser beams in optical (including fiberoptic) trains and in the atmosphere have become hot topics in laser science and engineering in the past few years. Single-mode output is mandatory for high-power CW laser applications in the military field. Moreover, an unstationary, dynamic operation regime is typical. Recognized devices and procedures for laser-beam diagnostics could not be directly applied because of dynamic behavior and untypical non-Gaussian profiles. 2) Methods: the Wigner transform approach was proposed to characterize dynamically variable high-power CW laser beams with significant deterministic aberrations. Wavefront-sensing measurements by means of the Shack-Hartmann method and decomposition into an orthogonal Zernike basis were applied. 3) Results: deterministic aberration as a result of unstationary thermal-optic effects depending on the averaged power of the laser output was found. Beam quality determined via the Wigner approach was changed in the same way as the measurements of the beam diameter in the far field. 4) Conclusions: such an aberration component seems to be the main factor causing degradation in beam quality and in brightness of high-power CW laser beams.