Golf balls incorporate thermoplastic compositions including urethane that is a reaction product of a diol or polyol with an isocyanate, and a peroxide to induce crosslinking. The polyol is selected from a polyester polyol, a polycarbonate polyol, a polyether polyol, a polybutadiene polyol or mixtures of these. Preferred chain extenders include polyols, diisocyanates, diamines or mixtures of these. The peroxide is selected from aliphatic peroxides, aromatic peroxides, cyclic peroxides, or mixtures of these. Upon sufficient heating of a composition of the thermoplastic urethane and peroxide, crosslinking is induced in the thermoplastic urethane to form a thermoset polyurethane. The invention allows for the processing advantages of a thermoplastic urethane with the superior performance characteristics of a thermoset polyurethane.