We study the thermal properties of a bulk Ni₅₅Fe₁₉Ga₂₆ Heusler alloy in a conduction calorimeter. At slow heating and cooling rates (∼1Kh^-1), we compare as-cast and annealed samples. We report a smaller thermal hysteresis after the thermal treatment due to the stabilization of the 14 M modulated structure in the martensite phase. In ultraslow experiments (40mKh^-1), we detect and analyze the calorimetric avalanches associated with the direct and reverse martensitic transformation from cubic to 14 M phase. This reveals a distribution of events characterized by a power law with exponential cutoff p(u)∝u^-εexp(-u/ξ) where ε∼2 and damping energies ξ=370μJ (direct) and ξ=27μJ (reverse) that characterize the asymmetry of the transformation.