  We investigate coupled spin and heat transport in easy-plane magnetic
insulators. These materials display a continuous phase transition between
normal and condensate states that is controlled by an external magnetic field.
Using hydrodynamic equations supplemented by Gross-Pitaevski phenomenology and
magnetoelectric circuit theory, we derive a two-fluid model to describe the
dynamics of thermal and condensed magnons, and the appropriate boundary
conditions in a hybrid normal-metal|magnetic-insulator|normal-metal
heterostructure. We discuss how the emergent spin superfluidity can be
experimentally probed via a spin Seebeck effect measurement.
