  Motivated by recent pump-probe spectroscopies, we study the effect of phonon
dissipation and potential cooling on the nonequilibrium distribution function
in a Floquet topological state. To this end, we apply a Floquet kinetic
equation approach to study two dimensional Dirac fermions irradiated by a
circularly polarized laser, a system which is predicted to be in a laser
induced quantum Hall state. We find that the initial electron distribution
shows an anisotropy with momentum dependent spin textures whose properties are
controlled by the switching-on protocol of the laser. The phonons then smoothen
this out leading to a non-trivial isotropic nonequilibrium distribution which
has no memory of the initial state and initial switch-on protocol, and yet is
distinct from a thermal state. An analytical expression for the distribution at
the Dirac point is obtained that is relevant for observing quantized transport.
