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The thermal inertia of an asteroid is an indicator of the thermophysical properties of the regolith and is determined by the size of grains on the surface. Previous thermophysical modeling studies of asteroids have identified or suggested that object size, rotation period, and heliocentric distance (a proxy for temperature) as important factors that separately influence thermal inertia. In this work we present new thermal inertias for 239 asteroids and model all three factors in a multi-variate model of thermal inertia. Using multi-epoch infrared data of a large (239) set of objects observed by WISE, we derive the size, albedo, thermal inertia, surface roughness, and sense of spin using a thermophysical modelling approach that doesn't require a priori knowledge of an object's shape or spin axis direction. Our thermal inertia results are consistent with previous values from the literature for similarly sized asteroids, and we identify an excess of retrograde rotators among main-belt asteroids < 8 km. We then combine our results with thermal inertias from the literature to construct a multi-variate model and quantify the dependency on asteroid diameter, rotation period, and surface temperature. This multi-variate model, which accounts for co-dependencies between the three independent variables, identified asteroid diameter and surface temperature as strong controls on thermal inertia., accepted to Planetary Science Journal 12.06.2021