  We analyze the effects of modified gravity on specific heats of electrons and
ions, Debye temperature, crystallization process, and cooling mechanism in
white dwarfs. We derive the Lane-Emden-Chandrasekhar equation and relate it to
the cooling process equations for Palatini $f(R)$ gravity. Moreover, for the
first time in the literature, we show that the gravity model plays a crucial
role not only in the mass and size of the white dwarf, but also affects their
internal properties. We further demonstrate that modified gravity can decrease
the cooling age significantly.
