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The increasing penetration of distributed generation sources in low-voltage distribution grids, electric vehicles, and new appliances from the consumer side can generate short repetitive overloads on the low-voltage cable network. This work investigates the change in the dielectric properties of low-voltage cable insulation caused by short-term overloads, examining how the cable structure affects the dielectric characteristics of the cable specimens in the case of cyclic short-term thermal aging. PVC-insulated low-voltage cable samples were exposed to an accelerated aging test in a temperature-controlled oven after changing their structures by removing different layers. Three aging cycles, each of six hours, were applied to the samples. After each cycle, the tan $\delta$ and capacitance were measured by an Omicron DIRANA Dielectric Response Analyzer in the laboratory at room temperature 24 $\pm 0.5$ °C. Furthermore, the polarization and depolarization currents were also studied. The results show that changing the cable structure impacts the dielectric parameters; in particular, the effect of the belting layer is significant. From the point of view of aging, the PVC belting layer protects the diffusion of the plasticizers of the inner structure. The findings of the study show that an asymmetric aging phenomenon can be observed in different polymeric components of the cables, even though the cables were aged in an air-circulated oven ensuring a homogeneous temperature distribution in the samples. Full article