A red star could be a tiny red dwarf, a star of feeble energy production and a small surface or a bloated giant or even supergiant star such as Antares or Betelgeuse, either of which generates far greater energy but passes it through a surface so large that the star radiates little per unit of surface area.
He is later confronted by Communications officer Lieutenant Thomas Keefer (Fred MacMurray) in the shower: "Sure we pick up the skeds from the Betelgeuse. They guard for all destroyers in port. It's standard procedure," shouts Keefer.