This paper presents a new formulation, based on Lagrangian coordinates, for the vibration of plates, both finite and infinite, at varying temperatures. The formulation circumvents a possible difficulty in applying perturbation theory to the usual formulae for infinite plates in a purely mechanical way. Knowledge of the thermal expansion tensor of the material is not required to infer the frequency-temperature behavior for arbitrary orientation of crystal, once experimental results have been established for a few chosen orientations; this contrasts with earlier work. The formulation is also immediately suitable for use in conjuction with the finite element method to obtain the variation of resonant frequency with temperature of finite plates, either with or without mass loading. Results are given for a particular A T-cut quartz resonator.