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There is no industry accepted analytical model to compute the critical temperature differential for the buckling of an unloaded curved track in North American literature. In this paper, the critical temperature differential for the buckling of an unloaded curved track is formulated by incorporating a value of unity for the factor of safety in the previously developed formula, which was developed considering thermal loading only. The factor of safety was the ratio between the resistance of a tie in an unloaded track against lateral displacement in the ballast and the lateral thermal load on a tie. The derived formula of the critical temperature differential for the buckling of an unloaded curved track is simple opposed to a complicated formula endorsed in the current European literature from 1969. The new formula is also validated in this paper. The critical temperature differentials for buckling of sharp and super-sharp curves have significant implications for track design and maintenance.