  We study the bispectrum of the primordial curvature perturbation on
uniform-density hypersurfaces generated by a kind of the noncanonical warm
inflation, wherein the inflation is provided by a noncanonical scalar inflaton
field that is coupled to radiation through a thermal dissipation effect. We
obtain an analytic form for the nonlinear parameter $f_{NL}$ that describes the
non-Gaussianity in first-order cosmological perturbation theory and analyse the
magnitude of this nonlinear parameter. We make a comparison between our result
and those of the standard inflation and the canonical warm inflation. We also
discuss when the contribution to the non-Gaussianity due to the second-order
perturbation theory becomes more important and what effect can be observed. We
take the Dirac-Born-Infeld (DBI) inflation as a concrete example to find how
the sound speed and the thermal dissipation strength to decide the
non-Gaussianity and to get a lower bound of the sound speed constrained by
PLANCK.
