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High-entropy alloys (HEAs) represent an important class of structural materials because of their high strength, ductility, and thermal stability. Understanding the mechanical response of isolated phases of a FCC/BCC dual-phase HEA is integral to understanding the mechanical properties of these alloys in the bulk. We investigate the compressive response of single-crystalline cylinders with diameters between 400 nm and 2 μm excised from individual grains within FCC and BCC phases of the dual-phase Al0.7CoCrFeNi HEA at 295 K, 143 K, and 40 K. We observed a “smaller is stronger” size effect in the yield strength as a function of pillar diameter, D, of both alloy phases for all temperatures, with a power-law exponent, m, decreasing with temperature for the FCC phase, and remaining constant for all temperatures in the BCC phase. We found reduced work-hardening rates and more extensive strain bursts during deformation at lower temperatures in all samples. We performed molecular dynamics simulations of similar FCC and BCC HEA compression that displayed deformation dominated by dislocation slip at all temperatures. We discussed theories of low-temperature strengthening in HEAs, compared them to our experimental data and assessed how they manifest in the observed temperature-dependent size effect and work-hardening.