A method and an arrangement for temperature compensation at circular resonators with dual mode utilization, which includes a material with a low coefficient of thermal expansion and for which the tensile or compressive forces are transferred to the resonator wall and produce elastic deformations there. The resonator wall is deformed in two mutually perpendicular directions in each case by the same absolute amount at one or more places along the axial extent, the deformation forces being introduced into the resonator war over at least one flange. This has the advantage that the peripheral shape of the casing of the circular resonator is deformed so that both orthogonal dual modes experience uniform shortening with simultaneous expansion of the material, as a result of which a high compensation effect is achieved.