The voltage fluctuations in the nanometer-thick nickel thin films, arising during direct current passing through a films sample, have been studied in the process of slow thermal heating. It has been shown that the positive voltage surges are determined by the resistance increase in the local area of the investigated film due to its local thinning and the appearance of ruptures as a result of the melting process start. The melting process beginning temperature has been measured for the nanometer-thick nickel films on silicon oxide. For 5, 20 and 40-nm-thick Ni films the melting start temperatures are 740, 815 and 875 K, respectively.