In recent times, astounding observations of both over- and under-luminous type Ia supernovae have emerged. These peculiar observations hint not only at surpassing the Chandrasekhar limit but may also suggest potential modifications in the physical attributes of their progenitors such as their cooling rate. This, in turn, can influence their temporal assessments and provide a compelling explanation for these intriguing observations. In this spirit, we investigate here the cooling process of white dwarfs in [Formula: see text] gravity with the simplest model [Formula: see text], where [Formula: see text] is the model parameter. Our modeling suggests that the cooling timescale of white dwarfs exhibits an inverse relationship with the model parameter [Formula: see text]. This unveils that in the realm of [Formula: see text] gravity, the energy release rate for white dwarfs increases as [Formula: see text] increases. Furthermore, we also report that the luminosity of the white dwarfs also depends on [Formula: see text] and an upswing in [Formula: see text] leads to an amplification in the luminosity. As a result, utilizing white dwarf luminosity could possibly define bounds on [Formula: see text] gravity models.