  In quantum gravity phenomenology, the effect of the generalized uncertainty
principle (GUP) on white dwarfs has been given much attention in the
literature. However, these studies assume a zero temperature equation of state
(EoS), consequently excluding young white dwarfs whose initial temperatures are
substantially high. To that cause, this paper calculates the Chandrasekhar EoS
and resulting mass-radius relations of finite temperature white dwarfs modified
by the quadratic GUP, an approach that extends Heisenberg's uncertainty
principle by a quadratic term in momenta. The EoS was first approximated by
treating the quadratic GUP parameter as perturbative, causing the EoS to
exhibit expected thermal deviations at low pressures, and conflicting behaviors
at high pressures, depending on the order of approximation. We then proceeded
with a full numerical simulation of the modified EoS, and showed that in
general, finite temperatures cause the EoS at low pressures to soften, while
the quadratic GUP stiffens the EoS at high pressures. This modified EoS was
then applied to the Tolman-Oppenheimer-Volkoff equations and its classical
approximation to obtain the modified mass-radius relations for general
relativistic and Newtonian white dwarfs. The relations for both cases were
found to exhibit the expected thermal deviations at small masses, where
low-mass white dwarfs are shifted to the high-mass regime at large radii, while
high-mass white dwarfs acquire larger masses, beyond the Chandrasekhar limit.
Additionally, we find that for sufficiently large values of the GUP parameter
and temperature, we obtain mass-radius relations that are completely removed
from the ideal case, as high-mass deviations due to GUP and low-mass deviations
due to temperature are no longer mutually exclusive.
