A new thermally stable ternary mixture composed of ethylene carbonate, γ-butyrolactone and methyl propionate (1: 1: 1 by weight), named EGM, is proposed for use as an electrolyte with the new salt LiTDI at a concentration of 1 mol L−1. The EGM mixture has many advantages over the classical binary mixture EC/DMC (1:1 by weight) when LiTDI is used as single salt: (i) it remains liquid from −60 °C to 130 °C, (ii) it exhibits a higher conductivity (8.5 mS cm−1 vs. 6.8 mS cm−1 at 25 °C), (iii) a lower viscosity (2.4 mPa s vs. 2.8 mPa s at 25 °C) and, (iv) allows a better dissociation of LiTDI (37% vs. 31%). Cycling tests were performed using graphite/Li and LiNi1/3Mn1/3Co1/3O2 (NMC)/Li half-cells as well as graphite/NMC full cells. It was shown that this electrolyte provides fair capacity retention for both the graphite and the NMC electrode at high C rates: up to 10C for graphite/Li half-cells and up to 6C for NMC/Li half-cells. The graphite//LiTDI-EGM//NMC full cell was able to sustain more than 800 cycles with a capacity retention of 70%, which is more than what was obtained in the same conditions with a graphite//LiPF6-EC/DMC//NMC cell (560 cycles). The impact on the discharge capacities of high (60 °C) and low (−20 °C) applied temperatures is also discussed herein.