The evolutions of magnetic properties at low temperatures and the influence of magnetic field on the temperature dependence of specific heat in martensitic Ni2Mn1.4Sn0.6 Heusler alloy are studied. The frequency-dependent blocking temperature and considerable exchange bias below it are measured in the martensitic phase. From the analysis of the specific heat curves under magnetic field, a large inverse magnetocaloric effect manifested as the magnetic field induced rise of isothermal magnetic entropy and/or magnetic field induced adiabatic temperature decrease in the vicinity of the reverse magnetostructural transformation and a significant value of the conventional magnetocaloric effect at the Curie temperature are obtained. The Debye temperature and electronic coefficient equal to ΘD=310±2 K and γ= 16.6±0.3 mJ/K2mol, respectively, do not depend on the magnetic field.