The heat capacity of the mass selected Na(41) (+) cluster has been measured using a differential nanocalorimetry method. A two-peak structure appears in the heat capacity curve of Na(41) (+), whereas Schmidt and co-workers [M. Schmidt, J. Donges, Th. Hippler, and H. Haberland, Phys. Rev. Lett. 90, 103401 (2003)] observed, within their experimental accuracy, a smooth caloric curve. They concluded from the absence of any structure that there is a second order melting transition in Na(41) (+) with no particular feature such as premelting. The observed difference with the latter results is attributed to the better accuracy of our method owing to its differential character. The two structures in the heat capacity are ascribed to melting and premelting of Na(41) (+). The peak at lower temperature is likely due to an anti-Mackay to Mackay solid-solid transition.