Networks of cylindrical membrane tubules appear in many intra-cellular organelles, such as Golgi, ER and mitochondria, and have also been recreated artificially in vitro. These tubules are pulled by molecular motors along filaments of the cytoskeleton, including both actin and microtubules. We propose here a model that is an extension of the thermodynamic equilibrium treatment of such membrane tubules. We treat the active, motors-induced motion of the tubule free ends through the use of an “effective temperature” describing this motion. This mean-field treatment allows us to calculate the effects of such active motion on the phase diagram of the tubules, demonstrating the control that the cell can exert on the morphology of intracellular membrane networks. We compare these results to recent observations of the ER network in cells.