Accurate control of fluid transport in nanoscale structures is key to enable the design of foreseeable nanofluidic devices with applications in many fields such as chip cooling, energy conversion, drug delivery and medical diagnosis. Here, inspired by the experimental observation of intrinsic thermal ripples in graphene and by recent advances in the manipulation of 2D nanomaterials, we introduce a graphene-based thermal nanopump which produces controlled and continuous liquid flow in nanoslit channels. We investigate the performance of this thermal nanopump employing large scale molecular dynamics simulations. Upon systematically imposing thermal gradients, a net water flow towards the low-temperature zone is observed, achieving flow velocities up to 4 m s-1. We observe that water flow rates increase monotonically due to larger ripple fluctuations on the graphene layers as higher thermal gradients are applied. Moreover, we find that the out-of-plane flexural phonons in graphene are responsible for flow generation wherein lower frequency phonon branches are activated with higher imposed thermal gradients. Furthermore, by modifying the wettability of the channel walls, an increase of 50% in the water flow rates is observed, showing that the efficiency of the proposed thermal pump can be enhanced by tuning the channel wall hydrophobicity. Our results indicate that thermal gradients can be employed to drive continuous water flow in graphene nanoslit channels with potential applications in nanofluidic devices.