  We analyze the dynamics of models of warm inflation with general dissipative
effects. We consider phenomenological terms both for the inflaton decay rate
and for viscous effects within matter. We provide a classification of the
asymptotic behavior of these models and show that the existence of a late-time
scaling regime depends not only on an asymptotic behavior of the scalar field
potential, but also on an appropriate asymptotic behavior of the inflaton decay
rate. There are scaling solutions whenever the latter evolves to become
proportional to the Hubble rate of expansion regardless of the steepness of the
scalar field exponential potential. We show from thermodynamic arguments that
the scaling regime is associated to a power-law dependence of the
matter-radiation temperature on the scale factor, which allows a mild variation
of the temperature of the matter/radiation fluid. We also show that the late
time contribution of the dissipative terms alleviates the depletion of matter,
and increases the duration of inflation.
