Operating temperature greatly influences the performance of supercapacitors. In order to achieve a very consistent performance at various working temperatures, we develop a low-cost and high performance supercapacitor utilizing graphene-based electrodes and Li2SO4-based aqueous electrolyte. The fabricated supercapacitor shows excellent charge storage characteristics from -20 degrees C to 45 degrees C. Specific capacitance of the electrode obtained from charge-discharge measurements, which are carried on two electrode cells, is 91 F/g at room temperature and there is no significant change observed when tested at various environments in a large temperature range (e.g. 74 F/g and 99 F/g at -20 degrees C and 45 degrees C, respectively). This supercapacitor also exhibits an outstanding capacitance retention and cycleability during its operation at different temperatures. Impedance measurements reveal the exceptionally low equivalent series resistance (ESR) and charge transfer resistance of the supercapacitor electrodes. Study of the relationship between charge storage and temperature by employing Arrhenius-type equation shows very low activation energy for the charge storage process. The remarkable electrochemical performances obtained here elucidate the great potential of the graphene-based supercapacitor for the efficient energy storage at various environmental temperatures.