Surface acoustic waves (SAWs) have significant potential for energy-efficient control of magnetic domain walls (DWs) owing to the magnetoelastic coupling effect. However, the dissipation of radio- frequency (rf) power in a SAW device can result in heating, which can also affect the DW motion. In this work, the heating of a SAW device consisting of a Pt/Co/Ta thin film with perpendicular magnetic anisotropy in between two interdigitated transducers is measured in situ with use of an on-chip Pt film as a thermometer within the SAW beam path. The application of SAWs at a center frequency of 48 MHz and a total rf power of 21 dBm results in a temperature increase of approximately 10 K within the SAW beam path owing to rf-power dissipation. DW velocity in a Pt/Co/Ta thin film is evaluated separately with use of Kerr microscopy at various temperatures or in the presence of SAWs. With a 10-K increase in temperature only, the DW velocity is found to increase from 33 ± 3 μm/s (at room temperature) to 104 ± 8 μm/s under an external magnetic field of 65 Oe. Traveling-SAW-assisted DW velocity (116 ± 3 μm/s) is slightly higher than that with a 10-K temperature increase alone, suggesting that the heating plays the major role in promoting DW motion, whereas the DW motion is significantly enhanced (418 ± 8 μm/s) in the presence of standing SAWs, indicating that magnetoelastic coupling is more important than heating in this scenario.