X-ray diffraction, thermogravimetric (TGA), differential scanning calorimetric (DSC), and impedance analysis were used to study the reported high-temperature phase transitions at 107, 149, 230, and 256 degrees C in crystals of cesium dihydrogen phosphate, CsH2PO4 (CDP). Our results show strong evidence that at all these temperatures, the observed DSC or differential thermal analysis (DTA) endothermic effects appear only as a consequence of a dehydration process starting on the surface of the crystal. Our results thus show that the reported transition at 230 degrees C is not a polymorphic transition. This means that the monoclinic symmetry, stable at room temperature, with space group P2(1/m)-C-2k(2), is maintained up to the final decomposition. Moreover, since we have not found any evidence for the existence of a superprotonic high-temperature phase above 230 degrees C, the high conductivity above 230 degrees C is thus only a consequence of the dehydration of the crystal surface.