Recent research findings indicate that the non-monotonic consumption of energy from lithium-ion (Li-ion) batteries results in a higher heat generation in electrical energy storage systems. During peak demands, a higher heat generation due to high discharging current increases the temperature from 80 °C to 120 °C, thereby resulting in thermal runaway. To address peak demands, an additional electrical energy storage component, namely supercapacitor (SC), is being investigated by various research groups. This paper provides insights into the capability of SCs in lightweight electric vehicles (EVs) to address peak demands using the worldwide harmonized light-duty driving test cycle (WLTC) driving profile in MATLAB/Simulink at different ambient temperatures. Simulation results indicate that temperature imposes a more prominent effect on Li-ion batteries compared with SCs under peak demand conditions. The effect of the discharging rate limit on the Li-ion battery current is studied. The result shows that SCs can accommodate the peak demands for a low discharging current limit on the battery, thereby reducing heat generation. Electrochemical impedance spectroscopy and cyclic voltammetry are performed on SCs to analyze their thermal performance at different temperatures ranging from 0 °C to 75 °C under different bias values of -0.6, 0, 0.6, and 1 V， respectively. The results indicate a higher specific capacitance of the SC at an optimum operation temperature of 25 °C for the studied bias. This study shows that the hybrid combination of the Li-ion battery and SC for a lightweight EV can address peak demands by reducing thermal stress on the Li-ion battery and increasing the driving range.