  We compute the primordial curvature spectrum generated during warm inflation,
including shear viscous effects. The primordial spectrum is dominated by the
thermal fluctuations of the radiation bath, sourced by the dissipative term of
the inflaton field. The dissipative coefficient \Upsilon, computed from first
principles in the close-to-equilibrium approximation, depends in general on the
temperature T, and this dependence renders the system of the linear
fluctuations coupled. Whenever the dissipative coefficient is larger than the
Hubble expansion rate H, there is a growing mode in the fluctuations before
horizon crossing. However, dissipation intrinsically means departures from
equilibrium, and therefore the presence of a shear viscous pressure in the
radiation fluid. This in turn acts as an extra friction term for the radiation
fluctuations that tends to damp the growth of the perturbations. Independently
of the T functional dependence of the dissipation and the shear viscosity, we
find that when the shear viscous coefficient \zeta_s is larger than 3 \rho_r/H
at horizon crossing, \rho_r being the radiation energy density, the shear
damping effect wins and there is no growing mode in the spectrum.
