  We use a quantum Monte Carlo method to study the ground state and
thermodynamic phase transitions of the spin supersolid phase in the S=1
Heisenberg model with uniaxial anisotropy. The thermal melting of the
supersolid phase shows unqiue signatures in experimentally measurable
observables. This Hamiltonian is a particular case of a more general and
ubiquitous model that describes the low energy spectrum of a class of {\it
isotropic} and {\it frustrated} spin systems. We also discuss some alternative
realizations of spin supersolid states in real magnets.
