  Departing from standard slow-roll conditions is one way of putting the
inflationary paradigm to test, and constraining the dynamics of the inflaton
field with a constant-rate of roll of the inflaton field, a.k.a. the
constant-roll scenario, is one way of exploring such deviation from the
standard slow-roll dynamics. In this manuscript we explore such a possibility
in a variant inflationary scenario, known as Warm Inflation. We construct and
derive the conditions for having constant-roll WI models where inflation lasts
at least for 60 $e-$folds, gracefully exits the constant-roll inflation phase,
and maintains near thermal equilibrium of the system which is an essential
feature of WI in the slow-roll regime. We show that while certain models of WI
(the ones with dissipative coefficient as a function of temperature alone) can
accommodate constant-roll dynamics, others (with dissipative coefficient as a
function of temperature and the inflaton field both) fail to maintain thermal
equilibrium once the constant-roll condition is imposed and hence cannot
produce a constant-roll WI phase.
