We report on resistivity, magnetic susceptibility, and very low-T specific
heat (C-p) of a i-AlPdRe quasicrytalline sample which, from resistivity mea
surements, is believed to lie on the insulating side of a metalinsulator (M
I) transition. We find an electronic contribution to C-p. which possibly ob
eys a gamma T variation above 1 K but follows a power Ta law (a similar to
0.1-0.3) below 1 K, in agreement with early results obtained for systems cr
ossing the MI transition. We point out the dependence of the lattice term o
n the method of sample preparation. Finally, from a comparative study of i-
AlCuFe and i-ALPdMn systems, we show that the large nuclear hyperfine speci
fic heat in AlPdRe, dominant below 300 mK, is of quadrupolar origin, due on
ly to the Re nuclei.