The insulation of the electrical equipment in medium and high-voltage grids is subjected to significant electrical and thermal stresses. The switching characteristic of the increasing number of power electronic devices in electric grids leads to the distortion of the voltage waveform which causes additional dielectric losses in insulation materials. The consequent dielectric heating and elevated temperatures present a risk of thermal breakdown and generally accelerated ageing. This manuscript presents how temperatures up to the glass transition and severely distorted sinusoidal voltages influence the dielectric losses in epoxy resin samples. The impact of additional dielectric losses is depicted and the risk of thermal runaway is assessed by comparing the distorted voltage stress to a pure sinusoidal oscillation. The ratio between the losses at distorted voltage and sinusoidal voltage declines with increasing temperature, reducing the risk of thermal runaway even at high temperatures and significant voltage distortion. A generalization of the risk assessment is given based on the discussion of the results and simple standardized measurement techniques.