Brownian thermal noise in dielectric multilayer coatings limits the sensitivity of current and future interferometric gravitational wave detectors. In this work we explore the possibility of improving the mechanical losses of tantala, often used as the high refractive index material, by depositing it on a substrate held at elevated temperature. Promising results have been previously obtained with this technique when applied to amorphous silicon. We show that depositing tantala on a hot substrate reduced the mechanical losses of the as-deposited coating, but subsequent thermal treatments had a larger impact, as they reduced the losses to levels previously reported in the literature. We also show that the reduction in mechanical loss correlates with increased medium range order in the atomic structure of the coatings using x-ray diffraction and Raman spectroscopy. Finally, a discussion is included on our results, which shows that the elevated temperature deposition of pure tantala coatings does not appear to reduce mechanical loss in a similar way to that reported in the literature for amorphous silicon; and we suggest possible future research directions.