  The Navier--Stokes order hydrodynamic equations for a low-density driven
granular mixture obtained previously [Khalil and Garz\'o, Phys. Rev. E
\textbf{88}, 052201 (2013)] from the Chapman--Enskog solution to the Boltzmann
equation are considered further. The four transport coefficients associated
with the heat flux are obtained in terms of the mass ratio, the size ratio,
composition, coefficients of restitution, and the driven parameters of the
model. Their quantitative variation on the control parameters of the system is
demonstrated by considering the leading terms in a Sonine polynomial expansion
to solve the exact integral equations. As an application of these results, the
stability of the homogeneous steady state is studied. In contrast to the
results obtained in undriven granular mixtures, the stability analysis of the
linearized Navier--Stokes hydrodynamic equations shows that the transversal and
longitudinal modes are (linearly) stable with respect to long enough wavelength
excitations. This conclusion agrees with a previous analysis made for single
granular gases.
