Anomalous temperature dependence is observed in the shape of the condensed phase domains in Langmuir monolayer of amphiphilic monoglycerolether (1-hexadecyl-rac-glycerol) using Brewster angle microscopy. The domain shapes are elongated at a lower temperature in contrast to the known effect of line tension and dipolar repulsion. Quantum mechanical calculations of molecular dipole moments and the analysis on the basis of Grazing incidence X-ray diffraction data reveal that the azimuthal orientation of the molecule enhances the regular arrangement of in-plane dipole moment at lower temperatures, which dictates the anomalous shape transition. The result has significance in controlling the shapes of mesoscopic aggregates by tuning temperature and molecular structure.