  We look into the Mpemba effect---the initially hotter sample cools
sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas
particles interact among them via elastic collisions and also with a background
fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is
described by an Enskog--Fokker--Planck equation. The analysis is carried out in
the first Sonine approximation, in which the evolution of the temperature is
coupled to that of the excess kurtosis. This coupling leads to the emergence of
the Mpemba effect, which is observed in an early stage of the relaxation and
when the initial temperatures of the two samples are close enough. This allows
for the development of a simple theory, linearizing the temperature evolution
around a reference temperature---namely the initial temperature closer to the
asymptotic equilibrium value. The linear theory provides a semiquantitative
description of the effect, including expressions for the crossover time and the
maximum temperature difference. We also discuss the limitations of our
linearized theory.
