We investigate the thermodynamic properties of a field-induced supersolid phase in a 2D quantum antiferromagnet model. Using quantum Monte Carlo simulations, a very rich phase diagram is mapped out in the temperature—magnetic-field plane, with an extended supersolid region where a diagonal (solid) order coexists with a finite XY spin stiffness (superfluid). The various quantum and thermal transitions out of the supersolid state are characterized. Experimental consequences in the context of field-induced magnetization plateau materials are briefly discussed.