We present the measurements of electrical resistivity (rho), specific heat (C-P), Seebeck coefficient (S), as well as thermal conductivity (kappa) of the Heusler compounds Ni2+xMn1-xGa from 10 to 400 K. A series of Ni2+xMn1-xGa alloys were prepared with x=0, 0.04, 0.06, 0.10, 0.14, 0.18, and 0.24 to systematically study the effect of substitution on the martensitic and ferromagnetic transitions. Unusual sharp peaks were observed in both S and kappa around the martensitic transition temperature (T-M), while a noticeable change of slope was seen in S and kappa at the ferromagnetic transition temperature (T-C) in Ni2+xMn1-xGa with x < 0.14. For x >= 0.14 the structural and magnetic phase transitions were found to merge together, as noticed from the sharp changes in all measured physical quantities. Existence of premartensitic transition (T-P) was unambiguously resolved in the stoichiometric compound Ni2MnGa by the C-P measurement, although such a feature becomes less pronounced with increasing x and completely disappears for the compositions x >= 0.10. Significant thermal hysteresis loops between heating and cooling cycles appear in the vicinity of T-M, which is associated with the presence of 7-layer and 5-layer modulated structures. In addition, huge peaks were observed in the thermal conductivity near T-M. We connected this observation to the nesting of the Fermi-level density of states, which is appropriate for the Peierls transition.