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By reducing the thermal conductance of an insulator one can, e.g., improve the energy conversion efficiency of thermoelectric devices. Then, more waste heat can be converted into electricity, and there will be less need to burn fossil fuels that produce carbon dioxide emissions. I study controlling of thermal conductance in an insulating silicon nitride membrane by introducing a periodic structure that causes scattering, i.e., a phonon crystal. In addition, I study electrical properties of superconducting tunnel junctions. This gives information about how tunnel junctions can be used as thermometers, heaters and coolers in thermal conductance experiments.