Elevated thermal stress-related aging is significant on the oil-impregnated paper (OIP) used as insulation in high-pressure gas cables (HPGCs). The aim of this article is to develop a cheap alternative for lab dielectric measuring and characterizing temperature-dependent parameters for OIP. First, this article derives the operating thermal conditions of the grid-aged cable based on IEC standards after analyzing the loading data using machine learning techniques to determine the elevated temperature levels for the experiments. Second, a novel lab-fabricated inexpensive electronics circuit is developed for polarization and depolarization current (PDC) measurements which can be adapted for such measurements over expensive commercial devices. From the measured parameters, an extended three-branch Debye model is optimized using a developed error function approach based on the Akaike information criterion (AIC) and goodness of fit. The model indicated a reduction in the branch resistance with temperature elevation and aging, whereas the branch capacitance revealed an increasing trend. The resultant relaxation time (RC) showed a decrease overall. Last, a short-duration frequency domain spectrum was analyzed and extrapolated to obtain parameters for a wide range of frequencies and fit in a Cole-Cole model, derived for oil-paper insulation. The time constants obtained from this model also confirmed a reducing trend across the temperature and aging variations and the model parameter, the alpha coefficient showed a decreasing trend. Last, the effect of the measured dielectric parameters is reflected with breakdown values to investigate the effect of temperature on the electrical life of insulation.