  We extend the k-inflation which is a type of kinetically driven inflationary
model under the standard inflationary scenario to a possible warm inflationary
scenario. The dynamical equations of this warm k-inflation model are obtained.
We rewrite the slow-roll parameters which are different from the usual
potential driven inflationary models and perform a linear stability analysis to
give the proper slow-roll conditions in the warm k-inflation. Two cases, a
power-law kinetic function and an exponential kinetic function, are studied,
when the dissipative coefficient $\Gamma=\Gamma_0$ and $\Gamma=\Gamma(\phi)$,
respectively. A proper number of e-folds is obtained in both concrete cases of
warm k-inflation. We find a constant dissipative coefficient
($\Gamma=\Gamma_0$) is not a workable choice for these two cases while the two
cases with $\Gamma=\Gamma(\phi)$ are self-consistent warm inflationary models.
