An analysis is presented that addresses the grain growth in 0.5 mum thick Cu films on Si substrates. Samples were thermally cycled to several maximum temperatures up to 500 degreesC in order to identify the evolution of grain size with temperature. Grain-morphological studies by focussed ion beam microscopy, as well as transmission and scanning electron microscopy were performed before and after thermal cycling. Additionally, in-situ measurements of stress and resistivity were carried out. During the first heating up to 500 degreesC the grains grow from 60 nm to approximately the tenfold size. The enlargement occurs by the growth of a few grains which consume the surrounding (stagnant) fine-grained matrix until the large grains meet and the fine-grained matrix is completely consumed. No other texture components than {111} were found before and after thermal cycling. An estimation yields the grain-boundary energy as the decisive driving force for the abnormal grain growth observed.