  We calculate the contribution of the fluctuations with the thermal origin to
the inflationary nonGaussianity. We find that even a small component of
radiation can lead to a large nonGaussianity. We show that this thermal
nonGaussianity always has positive $f_{\rm NL}$. We illustrate our result in
the chain inflation model and the very weakly dissipative warm inflation model.
We show that $f_{NL}\sim {\cal O}(1)$ is general in such models. If we allow
modified equation of state, or some decoupling effects, the large thermal
nonGaussianity of order $f_{\rm NL}>5$ or even $f_{\rm NL}\sim 100$ can be
produced. We also show that the power spectrum of chain inflation should have a
thermal origin. In the Appendix A, we made a clarification on the different
conventions used in the literature related to the calculation of $f_{\rm NL}$.
