Thermal analysis, X-ray diffraction, and impedance analysis were used to study the high-temperature nature of the KDP-family compounds: KH2PO4 (KDP), RbH2PO4 (RDP) and CsH2PO4 (CDP). Our results show that the structural phase transition from tetragonal to monoclinic modification in RDP and RDP earlier reported at around T-p approximate to 180 degrees C and T-p approximate to 86 degrees C, respectively, does not exist. For CDP we found that the structural phase transition from a monoclinic to a cubic symmetry superprotonic phase above 230 degrees C does not take place. Instead, in close agreement with Lee's suggestion, we found evidence that at all these temperatures a partial polymerization takes place at reaction sites distributed on the surface of the samples.