  Warm natural inflation is studied for the case of the original cosine
potential. The radiation bath during inflation induces a dissipation (friction)
rate in the equation of motion for the inflaton field, which can potentially
reduce the field excursion needed for an observationally viable period of
inflation. We examine if the dissipation thus provides a mechanism to avoid the
large decay constant $f \gtrsim M_{\mathrm{pl}}$ of cold cosine natural
inflation. Whereas temperature independent dissipation has previously been
shown to alleviate the need for a trans-Planckian decay constant $f$, we
illustrate here the difficulties of accommodating a significantly sub-Planckian
decay constant ($f<10^{-1}M_{\mathrm{pl}}$) in the case of the following
temperature dependent dissipation rates, $\Gamma \propto T^c$, with
$c=\{1,3\}$. Such dissipation rates represent physically well-motivated
constructions in the literature. For each model, we map its location in the
$r$-$n_s$ plane and compare with Cosmic Microwave Background data. For $c=1 \,
(c=3)$, we find that agreement with CMB data requires that dissipation be in
the weak (moderate) regime and that the minimum allowed value of the decay
constant in the potential is $f_{\rm min} = 0.3 \, (0.8)\,M_{\mathrm{pl}}$
respectively.
