The subject of this article is the investigation of thermal stability of the phase composition and physical-mechanical properties of the cold-rolled high-entropy multicomponent CrMnFeCoNi$_{2}$Cu alloy. Non-equiatomic high-entropy CrMnFeCoNi$_{2}$Cu alloy is designed and fabricated by argon-arc smelting and room-temperature cold rolling up to 98% deformation. Thermal stability of phase composition, structure and physical-mechanical properties are studied after two-hour annealing at temperatures of 1073, 1173, 1273, 1373, 1473 K. As shown, the CrMnFeCoNi$_{2}$Cu alloy in deformed state contains two f.c.c. phases (named as f.c.c.$_1$ and f.c.c.$_2$). Annealing at 1273 K promotes the formation of f.c.c.$_2$ phase. After annealing above 1273 K, the f.c.c.$_1$ phase enriched with Cu, Ni, and Mn is precipitated at the grain boundaries. A substantial grain-size increasing is observed after annealing at 1173 K. Level of microhardness remains stable up to temperature of 1273 K (0.84T$_{melt}$). Effect of strengthening after cold plastic deformation is completely removed due to annealing at 1473 K for two hours. Recrystallization strain in high-entropy CrMnFeCoNi$_{2}$Cu alloy lasts much slower than in most steels and alloys.