  We consider warm inflation with a Dirac-Born-Infeld (DBI) kinetic term in
which both the nonequilibrium dissipative particle production and the sound
speed parameter slow the motion of the inflaton field. We find that a low sound
speed parameter removes, or at least strongly suppresses, the growing function
appearing in the scalar of curvature power spectrum of warm inflation, which
appears due to the temperature dependence in the dissipation coefficient. As a
consequence of that, a low sound speed helps to push warm inflation into the
strong dissipation regime, which is an attractive regime from a model building
and phenomenological perspective. In turn, the strong dissipation regime of
warm inflation softens the microscopic theoretical constraints on cold DBI
inflation. The present findings, along with the recent results from swampland
criteria, give a strong hint that warm inflation may consistently be embedded
into string theory.
