  The Boltzmann kinetic equation is considered to evaluate the first-order
contributions $T_i^{(1)}$ to the partial temperatures in binary granular
suspensions at low density. The influence of the surrounding gas on the solid
particles is modeled via a drag force proportional to the particle velocity
plus a stochastic Langevin-like term. The Boltzmann equation is solved by means
of the Chapman--Enskog expansion around the local version of the reference
homogeneous base state. To first-order in spatial gradients, the coefficients
$T_i^{(1)}$ are computed by considering the leading terms in a Sonine
polynomial expansion. In addition, the influence of $T_i^{(1)}$ on the
first-order contribution $\zeta^{(1)}$ to the cooling rate is also assessed.
Our results show that the magnitude of both $T_i^{(1)}$ and $\zeta^{(1)}$ can
be relevant for some values of the parameter space of the system.
