  The Navier-Stokes transport coefficients of a granular gas are obtained from
the Chapman-Enskog solution to the Boltzmann equation. The granular gas is
heated by the action of an external driving force (thermostat) which does work
to compensate for the collisional loss of energy. Two types of thermostats are
considered: (a) a deterministic force proportional to the particle velocity
(Gaussian thermostat), and (b) a random external force (stochastic thermostat).
As happens in the free cooling case, the transport coefficients are determined
from linear integral equations which can be approximately solved by means of a
Sonine polynomial expansion. In the leading order, we get those coefficients as
explicit functions of the restitution coefficient $\alpha$. The results are
compared with those obtained in the free cooling case, indicating that the
above thermostat forces do not play a neutral role in the transport. The
kinetic theory results are also compared with those obtained from Monte Carlo
simulations of the Boltzmann equation for the shear viscosity. The comparison
shows an excellent agreement between theory and simulation over a wide range of
values of the restitution coefficient. Finally, the expressions of the
transport coefficients for a gas of inelastic hard spheres are extended to the
revised Enskog theory for a description at higher densities.
