A study of heat capacity, thermal dilatation and sensitivity to hydrostatic and uniaxial pressure was carried out on single-crystal and ceramic samples of NH4HSeO4. The main parameters of low-temperature successive phase transitions B2 (T1) ↔ incommensurate IC (T2) ↔ ferroelectric P1 (T3) ↔ non-ferroelectric did not depend on the type of samples. The behavior of the volumetric strain and the results of direct measurements of T3(p) contributed to the resolution of the longstanding problem associated with the ambiguity of the sign of the corresponding volumetric baric coefficient. The role of thermal expansion anisotropy in the formation of the piezocaloric effect (PCE) near the ferroelectric phase transition at T3 has been studied. Due to the strong difference in the linear baric coefficients, the main contribution to the barocaloric effect (BCE) comes from the inverse intensive and extensive PCE associated with the a-axis. Compared to a single crystal, ceramics demonstrate lower BCE values, which, however, exist in a wider temperature range, which leads to close values of integral caloric parameters. The strong decrease in both BCE and PCE at low-temperature transformations in NH4HSeO4 compared to the ferroelectrics NH4HSO4 and NH4NH4SO4 is associated with a small change in entropy during three low-temperature phase transitions, ΣΔSi = 2.52 J/mol∙K, which is a consequence of a high degree of structural ordering in selenate as a result of a high-temperature transformation at T0 between the superionic and B2 phases, accompanied by a giant change in entropy, ΔS0≈Rln21.