  The stability of a discrete time crystal against thermal fluctuations has
been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert
equation of a periodically-driven classical system composed of interacting
spins, each of which couples to a thermal bath. It is shown that in the
thermodynamic limit, even though the long-range temporary crystalline order is
stable at low temperature, it is melting above a critical temperature, at which
the system experiences a non-equilibrium phase transition. The critical
behaviors of the continuous phase transition have been systematically
investigated, and it is shown that despite the genuine non-equilibrium feature
of such a periodically driven system, its critical properties fall into the 3D
Ising universality class with a dynamical exponent ($z=2$) identical to that in
the critical dynamics of kinetic Ising model without driving.
