The protonic conductivity of (NH4)3H(SO4)2 has been measured using the complex-admittance method in the frequency range 30 Hz-200 MHz and the temperature interval 290-500 K covering both the ferroelastic (A2/a) and the paraelastic (R3m) phases. The dc conductivity shows quasi-two-dimensional behaviour and in the trigonal paraelastic phase its values in the (001) plane are typically super-protonic (10-2 ≤ σ(001) ≤ 10-1 S cm-1) with low activation enthalpy Ha(001) = 0.24 eV. The temperature dependence of the monoclinic superstructure reflection 120 has been studied using elastic neutron diffraction. It was found that the observed anomalies of the macroscopic and microscopic quantities, such as the morphic birefringence and the high-frequency dielectric constant on the one hand and the diffusion proton dynamics as well as the integrated intensity of the reflection 120 on the other hand, show pronounced differences in their temperature evolution below the ferroelastic phase transition temperature. The neutron scattering results as well as the dielectric measurements indicate precursor effects above Tc. The results are discussed on the basis of a phenomenological two-order-parameter model for the D53d-C62h ferroelastic phase transition. It is argued that properties which originate from the disorder of the oxygen and proton subsystem can be described by irreducible representations of the wave vector at the Γ point and the L point of the Brillouin zone, while properties which originate from displacements of the heavy atoms (the displacement mode) are solely described by the wave vector at the L point of the Brillouin zone of the paraphase.