The phase transformation kinetics of LaFe$_{11.41}$Mn$_{0.30}$Si$_{1.29}$-H$_{1.65}$ magnetocaloric compound is addressed by low rate calorimetry experiments. Scans at 1 mK/s show that its first order phase transitions are made by multiple heat fllux avalanches. Getting very close to the critical point, the step-like discontinuous behavior associated with avalanches is smoothed out and thermal hysteresis disappears. This result is confirmed by magneto-resistivity measurements and allows to measure accurate values of the zero field hysteresis ($Delta T_{hyst}$ = 0.37 K) and of the critical field (H$_c$ = 1.19 T). The number and magnitude of heat flux avalanches change with magnetic field, showing the interplay between the intrinsic energy barrier between phases and the microstructural disorder of the sample.
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