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This study explores the synthesis and electrochemical performance of graphene oxide co-doped with sodium and potassium (Na–K–GO) as electrode materials for supercapacitors (SCs) designed to operate at 60°C over an extended voltage window. The Na–K–GO is employed as the electrode material, while a fluorine-free ionic liquid (IL), [P4444][MEEA]—comprising a tetrabutylphosphonium cation and a 2-2-(2-methoxyethoxy)ethoxy anion—served as the electrolyte, enabling stable operation over a wide voltage window at elevated temperatures. Using this combination, three coin-cell SCs are fabricated: two symmetric devices (SC-1 and SC-2) and one asymmetric device (SC-3). All the three exhibited remarkable charge storage abilities, a retaining performance over 10 000 charge–discharge cycles at 60°C. Among the three devices, SC-3 exhibited the best overall electrochemical performance, delivering a high specific capacitance of 47.01 F g−1 and an energy density of 27.77 Wh kg−1 at 0.5 A g−1. Even at a higher current density of 1 A g−1, SC-3 maintained a maximum power density of 1000 W kg−1 while sustaining an energy density of 14.21 Wh kg−1, reflecting its strong rate capability. Moreover, the long-term cycling tests at 2 A g−1 demonstrated an outstanding durability of SC-3, which retained 99% coulombic efficiency after 10 000 cycles, significantly outperforming the SC-2 (90%) and SC-1 (79%).