  Radiative transfer is an important component of hydrodynamic simulations as
it determines the thermal properties of a physical system. It is especially
important in cases where heating and cooling regulate significant processes,
such as in the collapse of molecular clouds, the development of gravitational
instabilities in protostellar discs, disc-planet interactions, and planet
migration. We compare two approximate radiative transfer methods which
indirectly estimate optical depths within hydrodynamic simulations using two
different metrics: (i) the gravitational potential and density of the gas
(Stamatellos et al.), and (ii) the pressure scale-height (Lombardi et al.). We
find that both methods are accurate for spherical configurations e.g. in
collapsing molecular clouds and within clumps that form in protostellar discs.
However, the pressure scale-height approach is more accurate in protostellar
discs (low and high-mass discs, discs with spiral features, discs with embedded
planets). We also investigate the $\beta$-cooling approximation which is
commonly used when simulating protostellar discs, and in which the cooling time
is proportional to the orbital period of the gas. We demonstrate that the use
of a constant $\beta$ cannot capture the wide range of spatial and temporal
variations of cooling in protostellar discs, which may affect the development
of gravitational instabilities, planet migration, planet mass growth, and the
orbital properties of planets.
