  We present a numerical integration of the cosmological scalar perturbation
equations in warm inflation. The initial conditions are provided by a
discussion of the thermal fluctuations of an inflaton field and thermal
radiation using a combination of thermal field theory and thermodynamics. The
perturbation equations include the effects of a damping coefficient $\Gamma$
and a thermodynamic potential $V$. We give an analytic expression for the
spectral index of scalar fluctuations in terms of a new slow-roll parameter
constructed from $\Gamma$. A series of toy models, inspired by spontaneous
symmetry breaking and a known form of the damping coefficient, lead to a
spectrum with $n_s>1$ on large scales and $n_s<1$ on small scales.
