Harmonic distorted voltage waveforms can lead to excessive heat in the insulation of electrical equipment. The prospectively increasing number of power electronic devices in electrical grids requires the careful examination of the consequences of harmonics, which are introduced due to the operating principle of the semiconductor switches. Investigations of the thermal breakdown of solid dielectrics that may occur as a consequence of harmonic distortion on the voltage waveform of electrical grids are presented in this contribution. A thermo-electrical multi-frequency model allows the calculation of the overtemperature in the material. The calculations are confirmed by breakdown experiments of phenolic paper and epoxy resin. Generally, the additional dielectric losses due to the harmonic voltage distortion increase the possibility of exceeding the thermal equilibrium. However, modern insulation materials like the investigated epoxy resin have very low loss factors which is favourable for good thermal performance even with severely distorted voltages.