Recent works have shown that the thermal inertia of km-sized near-Earth asteroids (NEAs) is more than 2 orders of magnitude higher than that of main belt asteroids (MBAs) with sizes (diameters) between 200 and 1000 km. This confirms the idea that large MBAs, over hundreds millions of years, have developed a fine and thick thermally insulating regolith layer, responsible for the low values of their thermal inertia, whereas km-sized asteroids, having collisional lifetimes of only some millions years, have less regolith, and consequently a larger surface thermal inertia. Because it is believed that regolith on asteroids forms as a result of impact processes, a better knowledge of asteroid thermal inertia and its correlation with size, taxonomic type, and density can be used as an important constraint for modeling of impact processes on asteroids. However, our knowledge of asteroids' thermal inertia values is still based on few data points with NEAs covering the size range 0.1-20 km and MBAs that >100km. Here, we use IRAS infrared measurements to estimate the thermal inertia values of MBAs with diameters <100km and known shapes and spin vector, filling an important size gap between the largest MBAs and the km-sized NEAs. An update to the inverse correlation between thermal inertia and diameter is presented. For some asteroids thermophysical modeling allowed us to discriminate between the two still possible spin vector solutions derived from optical lightcurve inversion. This is important for (720) Bohlinia: our preferred solution was predicted to be the correct one by Vokrouhlický et al. [2003. The vector alignments of asteroid spins by thermal torques. Nature 425, 147-151] just on theoretical grounds.