We study the relevant parameters for the thermal Yarkovsky effect acting on Near-Earth Asteroids (NEAs) and Main Belt Asteroids (MBAs), specifically the rotation period and rotation axis. The study uses a quasi 3-D thermal model to derive the temperature map over the surface of the asteroid, and the thermal thrust is calculated. The results show how the thermal thrust is stronger for fast-rotating NEAs. However, the rotation period corresponding to maximal Yarkovsky efficiency increases with increasing semi major axis so that MBAs are more affected by Yarkovsky if they rotate at a rate of a few tens to hundreds of hours. This result suggests an excess of slow rotators on the far side of the main belt and explains the excess of fast rotators with retrograde spins in inner orbits.