Thin films (50-400 nm) of tosylate-doped poly(3,4-ethylene-dioxy-thiophene) (PEDOT) on various substrates have been studied by grazing incidence X-ray diffraction, using synchrotron radiation. The material was found to be highly anisotropic. This is correlated with a strong anisotropy observed in its optical and electronic properties. The crystalline order is limited, and evidence is found for a paracrystalline structure. A structural model is presented, which corroborates with the optical anisotropy. The effect of heating the material to 200 degrees C was studied. Unlike the situation for other substituted polythiophenes, heating PEDOT increases the crystalline order.