Near-Earth asteroid (469219) Kamo'oalewa (aka 2016 HO3) is an Earth co-orbital and a potential space mission target. Its short-term dynamics is characterized by a periodic switching between quasisatellite and horseshoe configurations. Due to its small diameter of only about 36 meters, the Yarkovsky effect may play a significant role in the long-term dynamics. In this work, we addressed this issue by studying the changes in the long-term motion of Kamo'oalewa caused by the Yarkovsky effect. We used an estimation of the magnitude of the Yarkovsky effect assuming different surface compositions and introduced the semi-major axis drift by propagating orbits of test particles representing the clones of the nominal orbit. Our simulations showed that the Yarkovsky effect may cause Kamo'oalewa to exit from the Earth co-orbital region a bit faster when compared to a purely gravitational model. Nevertheless, it still could remain an Earth companion for at least 0.5 My in the future. Our results imply that Kamo'oalewa is the most stable Earth's co-orbital object known so far, not only from a short-term perspective but also on long time scales.