Context. The mass loss of helium-burning stars, which are partially or completely stripped of their outer hydrogen envelope, is a catalyst of the cosmic matter cycle and decisive ingredient of massive star evolution. Yet, its theoretical fundament is only starting to emerge with major dependencies still to be uncovered. Aims: A temperature or radius dependence is usually not included in descriptions for the mass loss of classical Wolf-Rayet (cWR) stars, despite being crucial for other hot star wind domains. We thus aim to determine whether such a dependency will also be necessary for a comprehensive description of mass loss in the cWR regime. Methods: Sequences of dynamically consistent stellar atmosphere models were calculated with the hydrodynamic branch of the PoWR code along the temperature domain, using different choices for the luminosity, mass, and surface abundances. For the first time, we allowed nonmonotonic velocity fields when solving the hydrodynamic equation of motion. The resulting velocity structures were then interpolated for the comoving-frame radiative transfer, ensuring that the main wind characteristics were preserved. Results: We find a strong dependence of the mass-loss rate with the temperature of the critical/sonic point which mainly reflects the different radii and resulting gravitational accelerations. Moreover, we obtain a relation between the observed effective temperature and the transformed mass-loss rate Ṁt which seems to be largely independent of the underlying stellar parameters. The relation is shifted when different density contrasts are assumed for the wind clumping. Below a characteristic value of log (Ṁt [M⊙ yr−1]) −4.5, the slope of this relation changes and the winds become transparent for He II ionizing photons. Conclusions: The mass loss of cWR stars is a high-dimensional problem but also shows inherent scalings which can be used to obtain an approximation of the observed effective temperature. For a more realistic treatment of cWR stars and their mass loss in stellar evolution, we recommend the inclusion of a temperature dependency and ideally the calculation of hydrodynamic structure models.