High-entropy alloys, a new class of metallic materials, exhibit excellent mechanical properties at high temperatures. In spite of the worldwide interest, the underlying mechanisms for temperature dependence of mechanical properties of these alloys remain poorly understood. Here, we systemically investigate the mechanical behaviors and properties of Al1.2CrFeCoNi (comprising a body-centered cubic phase) and Al0.3CrFeCoNi (comprising a face-centered cubic phase) single-crystal micropillars with three orientations ([100], [110], and [111]) at temperatures varying from 300 to 675 K by using in situ compression of micropillars inside a scanning electron microscope. The results show that the yield stresses of Al1.2CrFeCoNi micropillars are insensitive to temperature changes, and their flow stresses and work hardening rates increase slightly with increasing temperature from 300 to 550 K, which differs from the typical temperature dependence of yield/flow stresses in metals and alloys. In contrast, Al0.3CrFeCoNi micropillars exhibit typical thermal softening. Furthermore, it is found that the Al1.2CrFeCoNi micropillars exhibit a transition from homogenous deformation to localized deformation at a critical temperature, while the Al0.3CrFeCoNi micropillars always maintain a well-distributed and fine slip deformation. Detailed transmission electron microscopy analyses reveal that dynamic recrystallization (involving dislocation tangles, and formation of dislocation cell structures and sub-grains) plays a key role in the observed temperature insensitivity of the yield stress and increasing flow stress (and work hardening rate) with increasing temperature in the Al1.2CrFeCoNi micropillars, and that thermally activated dislocation slip leads to thermal softening of the Al0.3CrFeCoNi micropillars. The differences in deformation modes and temperature dependence of the mechanical properties between Al1.2CrFeCoNi and Al0.3CrFeCoNi essentially originate from the differences in dislocation activities and slip systems since the two alloys adopt different phases. Our findings provide key insights in the temperature dependence of mechanical properties and deformation behaviors of high-entropy alloys with body-centered cubic and face-centered cubic phases.