  Neutron stars provide a unique physical laboratory to study the properties of
matter at high density. We study a diagnostic of the composition of
high-density matter, namely, g-mode oscillations, which are driven by buoyancy
forces. These oscillations can be excited by tidal forces and couple to
gravitational waves. We extend prior results for the g-mode spectrum of cold
neutron star matter to temperatures that are expected to be achieved in neutron
star mergers using a parameterization for finite-temperature effects recently
proposed by Raithel, \"Ozel and Psaltis. We find that the g-modes of canonical
mass neutron stars ($\approx$1.4$M_{\odot}$) are suppressed at high
temperature, and core $g$-modes are supported only in the most massive ($\geq
$2$M_{\odot}$) of hot neutron stars.
