  We study the power spectrum of the mass density perturbations in an inflation
scenario that includes thermal dissipation. We show that the condition on which
the thermal fluctuations dominate the primordial density perturbations can
easily be realized even for weak dissipation, i.e., the rate of dissipation is
less than the Hubble expansion. We find that our spectrum of primordial density
perturbations follows a power law behavior, and exhibits a ``thermodynamical''
feature -- the amplitude and power index of the spectrum depend mainly on the
thermodynamical variable $M$, the inflation energy scale. Comparing this result
with the observed temperature fluctuations of the cosmic microwave background,
we find that both amplitude and index of the power spectrum can be fairly well
fitted if $M \sim 10^{15}-10^{16}$ GeV.
