  We study a dilute granular gas immersed in a thermal bath made of smaller
particles with masses not much smaller than the granular ones in this work.
Granular particles are assumed to have inelastic and hard interactions, losing
energy in collisions as accounted by a constant coefficient of normal
restitution. The interaction with the thermal bath is modeled by a nonlinear
drag force plus a white-noise stochastic force. The kinetic theory for this
system is described by an Enskog--Fokker--Planck equation for the one-particle
velocity distribution function. To get explicit results of the temperature
aging and steady states, Maxwellian and first Sonine approximations are
developed. The latter takes into account the coupling of the excess kurtosis
with the temperature. Theoretical predictions are compared with direct
simulation Monte Carlo and event-driven molecular dynamics simulations. While
good results for the granular temperature are obtained from the Maxwellian
approximation, a much better agreement, especially as inelasticity and drag
nonlinearity increase, is found when using the first Sonine approximation. The
latter approximation is, additionally, crucial to account for memory effects
such as Mpemba and Kovacs-like ones.
