  We report low-temperature specific heat measurements in magnetic fields up to
12 T applied parallel and perpendicular to the tetragonal c-axis of the heavy
fermion superconductor Ce$_2$PdIn$_8$. In contrast to its quasi-two-dimensional
(2D) relative CeCoIn$_5$, the system displays an almost isotropic upper
critical field. While there is no indication for a FFLO phase in
Ce$_2$PdIn$_8$, the data suggest a smeared weak first-order superconducting
transition close to $H_{c2}\approx 2$ T. The normal state electronic specific
heat coefficient displays logarithmically divergent behavior, comparable to
CeCoIn$_5$ and in agreement with 2D quantum criticality of spin-density-wave
type.
