Ternary solutions of alpha-cyclodextrin (alphaCD) in 4-methylpyridine (4MP)/water mixtures solidify when heated and melt when cooled, and the crystalline solid phase exhibits a rich phase behavior as a function of temperature. In this work, we extend these earlier investigations to pure binary mixtures of alphaCD in water free 4MP, characterized via temperature and time dependent measurements of viscosity, X-ray diffraction, and infrared spectroscopy, complemented by observations of acoustic properties and small angle neutron diffraction. At high concentrations (>500 g l(-1)), these solutions enter an amorphous solid phase not only with decreasing but also with increasing temperature, before crystallizing at higher temperatures. This inverse solidification is attributed to the growth of hydrogen bonded clusters, leading to a steep increase of the viscosity with temperature.