The densest α modification of AlH(3) and AlD(3) is thermodynamically stable at high hydrogen pressures. At ambient pressure, α-AlH(3) and α-AlD(3) rapidly and irreversibly decompose to Al and H(2) or D(2) gas when heated to about 420 and 520 K, respectively. In the present paper, the heat capacities at constant volume (C(V)) and at constant pressure (C(P)) are calculated for α-AlH(3) and α-AlD(3) at a pressure of 1 atm and temperatures 0-1000 K using the phonon densities of states determined earlier by inelastic neutron scattering at helium temperatures (Kolesnikov et al 2007 Phys. Rev. B 76 064302). The C(P)(T) dependence of AlH(3) is also measured at temperatures 6-30 K and 130-320 K and that of AlD(3) at 130-320 K in order to compensate for the scatter in the literature data and to improve the accuracy of the calculated C(V) and C(P) dependences at low temperatures.