Planetary magma oceans are present throughout the Solar System in a variety of forms. Over time, these oceans pass through various evolutionary stages, influencing the dynamics of the planetary body in question. Magma ocean evolution is explored here in greater detail through a case study of a cryomagma ocean beneath the surface of Triton, Neptune's icy satellite. Triton is hypothesized to have experienced extensive tidal dissipation within its interior early during evolution. Given the influence of tidal dissipation, this study evaluates ocean sustainability using a parametrized turbulent convection model and a coupled crust-ocean evolution model. The latter model links the thermal evolution of the crust, solved as a Stefan problem, with the crystallizing multiphase ocean. Due to an evident 'tidal blanketing' effect, these models indicate that an ocean may survive around 1 billion years given Triton's present day orbit, a timescale that increases with increasing dissipation and orbital eccentricity.