Using our recent design of thermally managed sandwich device structures, we studied the radiation frequency characteristics of three such devices of the same rectangular dimensions made from the same single crystal of the high-T_c superconductor Bi₂Sr₂CaCu₂O_{8+ δ}, and all three devices exhibit similar characteristics. Their observed radiation intensities appear to be enhanced at many transverse magnetic TM_n,m cavity mode frequencies, possibly including some higher TM_0,m modes with waves solely along the rectangular length, none of which have previously been reported. In addition, the temperature dependences of the radiation frequencies correspond strongly to the temperature dependences of the maximum bias voltages applied to the devices. The excitations of many cavity modes higher in frequency than that of the usually observed TM_1,0 mode and the high reproducibility of the radiation frequency characteristics both appear to originate from the reduction in the Joule self-heating of the thermally managed sandwich structures. The information provided here should aid in the design of future devices to obtain the desired emission frequency ranges.