Polymer insulating materials such as cross linked polyethylene (XLPE) are employed in electric cables used for extra high voltage. These materials can degrade due to chemical, mechanical and electric stress, possibly caused by voids, the presence of extrinsic materials and protrusions. Therefore, this study measured discharge patterns, discharge phase angle, quantity and occurrence frequency as well as changes in XLPE under different temperatures and applied voltages. To quantitatively analyze the irregular partial discharge patterns measured, the discharge patterns were examined using a statistical program. A three layer sample was fabricated, wherein the upper and lower layers were composed of non-void XLPE, while the middle layer was composed of an air void and copper particles. After heating to room temperature and $50^{circ}C$ and $80^{circ}C$ in silicone oil, partial discharge characteristics were studied by increasing the voltage from the inception voltage to the breakdown voltage. Partial discharge statistical analysis showed that when the K-means clustering was carried out at 9 kV to determine the void discharge characteristics, the amount discharged at low temperatures was small but when the temperature was increased to $80^{circ}C$, the discharge amount increased to be 5.7 times more than that at room temperature because electric charge injection became easier. An analysis of the kurtosis and the skewness confirmed that positive and negative polarity had counterclockwise and clockwise clustering distribution, respectively. When 5 kV was applied to copper particles, the K-means was conducted as the temperature changed from $50^{circ}C$ to $80^{circ}C$. The amount of charge at a positive polarity increased 20.3% and the amount of charge at a negative polarity increased 54.9%. The clustering distribution of a positive polarity and negative polarity showed a straight line in the kurtosis and skewness analyses.