  A supernova event in our own galaxy will result in a large number of
neutrinos detected on Earth within the time-frame of a few seconds. These
neutrinos will have been produced thermally with, in principle, three distinct
temperatures for the electron, anti-electron and remaining heavy flavours
respectively. We revisit the possibility that new MeV-mass particles $\chi$ are
also produced thermally during the event, which scatter with the neutrinos and
alter their temperatures. Our main emphasis is on the detectability of this
effect using the neutrino spectrum, given the large uncertainty on the
temperature and density profiles of the stellar matter. By marginalising over
the parameters of a simple analytic model for the stellar profile, we find that
Super Kamiokande could place an upper limit on the scattering cross section at
the level of $\sigma_{\chi \nu} \sim 10^{-40} \cdot (T / \mathrm{MeV})^2$
cm$^2$ for 10 MeV mass particles at 90% confidence. A direct-detection-like
experiment would be less susceptible to systematic uncertainties in the
neutrino production and mixing, but this would need a target mass around 100
tonnes in order to acquire enough statistics to compete with Super Kamiokande.
