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Recently, a high-mobility surface conduction channel and in-gap states were identified in the correlated small-gap semiconductor FeSi using electrical transport measurements and high-resolution tunneling spectroscopy. The mobility of the charge carriers in the surface channel is quantitatively reminiscent of topological insulators, but displays a lack of sensitivity to the presence of ferromagnetic impurities as studied by means of a series of single crystals with slightly different starting compositions. Here, we report measurements of the specific heat of these crystals. At low temperatures, a shallow maximum is observed in the specific heat divided by temperature. This maximum is suppressed under magnetic field, characteristic of a Schottky anomaly associated with magnetic impurities. In comparison, the height of this maximum decreases with increasing initial iron content.