  We propose a new approach to constant-roll warm inflation as a generalization
of constant-roll inflation. Based on the $\beta$-function formalism, it is
shown that constant-roll warm inflation models with a natural end fall into
universality classes defined by three different types of $\beta$-functions,
under the assumption that radiation energy density is quasi-stable. Given that
warm inflation is completely specified by the $\beta$-function and dissipation
coefficient ratio, we investigate whether or not the inflation can physically
be realized for enough number of e-foldings at the background level for some
combinations of the $\beta$-functions and non-trivial dissipation coefficient
ratios.
