Thermophoresis is the phenomenon wherein particles experience a net drift induced by a thermal gradient. In this work, molecular dynamics simulations are conducted to study with atomistic detail the thermophoresis of water nanodroplets inside carbon nanotubes (CNTs) and its interplay with the retarding liquid-solid friction. Different applied temperatures, thermal gradients, and droplet sizes are used to reveal the dynamics of the two kinetic regimes of the thermophoretic motion in CNTs. The results indicate that during the droplet motion, the thermophoretic force is independent of the velocity of the droplet, whereas the magnitude of the retarding friction force exhibits a linear dependence. In fact, in the initial regime the magnitude of the friction force increases linearly with the droplet velocity, until the thermophoretic force is balanced by the friction force as the droplet reaches its terminal velocity in the final regime. In addition, an increase in the magnitude of the thermophoretic force is found for longer water droplets. These findings provide a deeper understanding of liquid transport driven by temperature gradients in nanoconfined geometries where liquid-solid interfaces govern fluidics.