Changes in the microstructure of ε-phase Pb-Bi films with various thicknesses that were deposited onto oxidized Si substrates and then repeatedly thermally cycled between 298 and 4.2 K were studied using x-ray diffraction, transmission, and scanning electron microscopy. The level of strain supported elastically by the films had a strong dependence on the film thickness. For 0.2-μm-thick films, almost all of the strain was supported elastically. For 1.0-μm-thick films most of the strain was relaxed upon cooling to 4.2 K, and grain rotation, hillock formation, and dislocation slip steps were observed after repeated cycling. For 0.4-μm-thick films in which about 0.1% of the strain was relaxed upon cooling to 4.2 K, such changes in the microstructure were observed after ∼200 cycles. Although these changes were significantly suppressed by 0.6-μm-thick SiO layers coated onto the films, the grain rotation and hillock formation were observed after 400 cycles for SiO-coated, 0.4-μm-thick films similar to those used for the counter electrodes of Pb-alloy Josephson junctions.