The ionic liquid 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide (BDMIM-TFSI) showed a conductivity of 1.65 mS cm−1 and an electrochemical stability window of 4.4 V at room temperature. Two types of electrodes based on carbon nanomaterials were prepared: (1) with alternating layers of two oppositely charged functionalized double-walled carbon nanotubes (DWCNTs) and (2) with the functionalized DWCNTs and graphene oxide nanoplatelets. The electrodes presented a porous morphology and a connected pathway between the carbon nanotubes and graphene oxide platelets. Electrochemical capacitors based on the carbon nanomaterials and BDMIM-TFSI were produced in a stacking configuration and were characterized at 25 °C, 60 °C, and 100 °C. The supercapacitors with electrodes based on the three alternating layers of two oppositely charged DWCNTs and graphene oxide presented higher values of capacitance, which were attributed to a morphology favorable to providing ionic access to the carbonaceous surface. Box-like voltammetric curves were used to calculate the capacitance in a 4-V potential window at 100 °C.