Context. Main belt comets represent a recently discovered class of objects. They are quite intriguing because, while having a Tisserand invariant value higher than 3, are showing cometary activity. Aims. We study the activity of the main belt comets making the assumption that they are icy-bodies and that the activity has been triggered by an impact. We try to determine the characteristics of this activity. We also try to determine if the nowadays impact rate in the main asteroid belt is compatible with the hypothesis of an activity triggered by a recent impact. Methods. Due to the fact that the main belt comets can be considered as a kind of comets, we apply a thermal evolution model developed for icy bodies in order to simulate their activity. We also apply a model to derive the impact rate, with respect to the size of the impactor, in the main belt. Results. We demonstrate that a stable activity can result from a recent impact, able to expose ice-rich layers, and that the impact rate in the main belt is compatible with this explanation.