Abstract: Results of low-temperature specific heat measurements (1.5-8.0 K) on X2MnSn (X = Co, Ni, Pd, Cu), X2Mnln (X = Ni, Pd) and Ni2MnSb Heusler compounds are presented. All the compounds, except the cobalt based one, exibit a lattice spectrum anomaly described by an Einstein's term (soft-phonons). For all but one compound, the experimental values of the electronic specific heat coefficients are, at least, twice as big as the theoretical estimates. For two compounds it was possible to determine the magnetic effective field on Mn nuclei.