Electrical conductivity of HVDC cable insulation materials is important for its function. It is very practical to evaluate this parameter by DC conductivity measurements on press molded polymeric plates samples. While in real operation conditions, the insulation undergoes both static and dynamic thermal conditions, most of the published research in this area is still focused only on steady state thermal conditions. In this work, the focus is instead on the behavior of electrical conductivity under dynamic thermal conditions. Press molded XLPE and LDPE plate samples with different preparations are tested under 25 kV/mm DC field with a dynamic temperature profile ranging from room temperature to 90 °C. It was discovered that in many cases, the measured conductivity during dynamic measurements strongly deviates from the expected Arrhenius temperature dependence; instead the conductivity shows a nonmonotonic temperature dependence manifested as conductivity peaks during heating and cooling. The behavior is found to be strongly related to the type of protective film used during press molding of the sample; further degassing leads to a reduction of the nonmonotonic temperature dependence and with long degassing the behavior tends to the expected Arrhenius temperature dependence.