By applying the lubrication approximation, an evolution equation for the position of the free interface of a rotating thin droplet is derived. The dynamic wetting of the droplet is modeled by using the empiric Tanner's law and the model is compared with experimental results taken from literature. A linear stability analysis gives the unstable modes and the onset of the fingering instability. Also convections due to the temperature dependency of surface tension and density as well as their stability are considered.