  The aim of this work is to explore the combined effect of polydispersity and
roughness on the partial energy production rates and on the total cooling rate
of a granular fluid mixture. We consider a mixture of inelastic rough hard
spheres of different number densities, masses, diameters, moments of inertia,
and mutual coefficients of normal and tangential restitution. Starting from the
first equation of the BBGKY hierarchy, the collisional energy production rates
associated with the translational and rotational temperatures ($T_i^\text{tr}$
and $T_i^\text{rot}$) are expressed in terms of two-body average values. Next,
those average values are estimated by assuming a velocity distribution function
based on maximum-entropy arguments, allowing us to express the energy
production rates and the total cooling rate in terms of the partial
temperatures and the parameters of the mixture. Finally, the results are
applied to the homogeneous cooling state of a binary mixture and the influence
of inelasticity and roughness on the temperature ratios
$T_1^\text{tr}/T_1^\text{rot}$, $T_2^\text{tr}/T_1^\text{tr}$, and
$T_2^\text{rot}/T_1^\text{rot}$ is analyzed.
