A detailed low energy electron diffraction analysis has been performed to investigate the adsorption of potassium on Al(111) at 90 K and at 300 K. At each temperature a (square-root 3 x square-root 3)R30-degrees structure is formed, however, the adsorbate positions are different. For adsorption at 90 K the adatoms occupy on-top sites and at 300 K they occupy substitutional sites, both geometries have hitherto been regarded as very unusual. An irreversible phase transition from the former to the latter stable structure occurs on warming to 300 K. The obtained interatomic distances and surface relaxations are discussed in terms of an interplay of the electrostatic repulsion between adatoms and substrate screening as well as coordination number. An approximate scheme for including the effect of anisotropic atomic motions under the influence of thermal excitation was applied. It is found that the R factors for the on-top site are significantly improved whereas no improvement is found for the substitutional site.