We present a dynamical analysis of the galaxy cluster Abell 970 based on a new set of radial velocities measured at ESO, Pic du Midi and Haute-Provence observatories. Our analysis indicates that this cluster has a substructure and is out of dynamical equilibrium. This conclusion is also supported by differences in the positions of the peaks of the surface density distribution and X-ray emission, as well as by the evidence of a large scale velocity gradient in the cluster. We also found a discrepancy between the masses inferred with the virial theorem and with the X-ray emission, what is expected if the galaxies and the gas inside the cluster are not in hydrostatic equilibrium. Abell 970 has a modest cooling flow, as is expected if it is out of equilibrium as suggested by Allen (1998). We propose that cooling flows may have an intermittent behavior, with phases of massive cooling flows being followed by phases without significant cooling flows after the acretion of a galaxy group massive enough to disrupt the dynamical equilibrium in the center of the clusters. A massive cooling flow will be established again, after a new equilibrium is achieved.