Heteroepitaxy of β-phase gallium oxide (β-Ga2O3) thin films on foreign substrates shows promise for the development of next-generation deep ultraviolet solar blind photodetectors and power electronic devices. In this work, the influences of the film thickness and crystallinity on the thermal conductivity of (2̅01)-oriented β-Ga2O3 heteroepitaxial thin films were investigated. Unintentionally doped β-Ga2O3 thin films were grown on c-plane sapphire substrates with off-axis angles of 0° and 6° toward ⟨112̅0⟩ via metal–organic vapor phase epitaxy (MOVPE) and low-pressure chemical vapor deposition. The surface morphology and crystal quality of the β-Ga2O3 thin films were characterized using scanning electron microscopy, X-ray diffraction, and Raman spectroscopy. The thermal conductivities of the β-Ga2O3 films were measured via time-domain thermoreflectance. The interface quality was studied using scanning transmission electron microscopy. The measured thermal conductivities of the submicron-thick β-Ga2O3 thin films were relatively low as compared to the intrinsic bulk value. The measured thin film thermal conductivities were compared with the Debye–Callaway model incorporating phononic parameters derived from first-principles calculations. The comparison suggests that the reduction in the thin film thermal conductivity can be partially attributed to the enhanced phonon-boundary scattering when the film thickness decreases. They were found to be a strong function of not only the layer thickness but also the film quality, resulting from growth on substrates with different offcut angles. Growth of β-Ga2O3 films on 6° offcut sapphire substrates was found to result in higher crystallinity and thermal conductivity than films grown on on-axis c-plane sapphire. However, the β-Ga2O3 films grown on 6° offcut sapphire exhibit a lower thermal boundary conductance at the β-Ga2O3/sapphire heterointerface. In addition, the thermal conductivity of MOVPE-grown (2̅01)-oriented β-(AlxGa1–x)2O3 thin films with Al compositions ranging from 2% to 43% was characterized. Because of phonon-alloy disorder scattering, the β-(AlxGa1–x)2O3 films exhibit lower thermal conductivities (2.8–4.7 W/m·K) than the β-Ga2O3 thin films. The dominance of the alloy disorder scattering in β-(AlxGa1–x)2O3 is further evidenced by the weak temperature dependence of the thermal conductivity. This work provides fundamental insight into the physical interactions that govern phonon transport within heteroepitaxially grown β-phase Ga2O3 and (AlxGa1–x)2O3 thin films and lays the groundwork for the thermal modeling and design of β-Ga2O3 electronic and optoelectronic devices.