A series of thermoplastic polymer electrolytes have been prepared employing poly(ethylene oxide) (PEO) as a polymer matrix, bis(trifluoromethane sulfonimide) (LiTFSI), and different room-temperature ionic liquids (RTIL) with bis(fluorosulfonyl)imide (FSI) or TFSI anions. This formulation makes them safe and non-flammable. The electrolytes have been processed in the absence of solvents by melt compounding at 120 °C, using sepiolite modified with d-α-tocoferol-polyethyleneglycol 1000 succinate (TPGS-S) as a physical cross-linker of PEO. Several concentrations of RTILs, lithium salt, and TPGS-S have been tested in order to obtain the highest ionic conductivity (σ) without losing electrolytes’ mechanical stability. The materials’ rheology and ionic conductivity have been extensively characterized. The excellent crosslinking ability of TPGS-S makes the electrolytes behave as thermoplastic materials, even those with the highest liquid concentration. The electrolytes with the highest concentrations of FSI anion present a σ over
10−3 S·cm−1 at 25 °C and close to 10−2 S·cm−1 at 70 °C, and notably behave as solids at temperatures up to 90 °C despite over 65 wt % of their formulation being liquid. The electrolytes thus obtained are safe solid thermoplastics prepared by industrially scalable procedures and are suitable for energy storage devices, proving the adequacy of polymer-based materials as solid electrolytes for batteries or supercapacitors.