A new approach to the solution of the problem of wrinkling in sandwich structures subject to a combination of compressive stresses and uniform elevated temperature is presented. The solution is based on the assumption that both facings wrinkle simultaneously, that is, wrinkling of one of the facings triggers wrinkling of the opposite facing. This approach eliminates shortcomings of several previously developed models where the effect of wrinkling on the opposite facing was disregarded. The solution for the stresses in the core is obtained based on the theory of elasticity. Subsequently, the combination of wrinkling loads, including thermal contributions, is determined either by the energy method or from the equations of equilibrium of the facings. It is shown that in the particular case of a thick and compliant core, the present method yields the results that are almost identical to the well-known Plantema solution. As follows from the numerical analysis, the wrinkling stress increases with the facing-to-core thickness ratio. Elevated temperature results in a decrease of the applied mechanical stress corresponding to wrinkling. In the representative examples, this decrease was almost proportional to temperature.