Administration of temperature-responsive drug carriers that release anticancer drugs at high temperatures can benefit hyperthermia therapies because of the synergistic effect of anticancer drug molecules and high temperature on killing the cancer cells. In this study, we design and characterize a new temperature-responsive nanocarrier based on a naturally occurring and biocompatible clay mineral, halloysite nanotubes. Poly(N-isopropylacrylamide) brushes were grown on the surface of halloysite nanotubes using a combination of mussel-inspired dopamine polymerization and surface-initiated atom transfer radical polymerization. The chemical structure of the hybrid materials was investigated using X-ray photoelectron spectroscopy, thermogravimetric analysis and energy-dispersive X-ray spectroscopy. The hybrid material was shown to have a phase transition temperature of about 32 °C, corresponding to a 40 nm thick polymer layer surrounding the nanotubes. Cell studies suggested that grafting of poly(N-isopropylacrylamide) brushes on the polydopamine-modified halloysite nanotubes suppresses the cytotoxicity caused by the polydopamine interlayer and drug release studies on nanotubes loaded with doxorubicin showed that thanks to the poly(N-isopropylacrylamide) brushes a temperature-dependent drug release is observed. Finally, a fluorescent dye molecule was covalently attached to the polymer-grafted nanotubes and stimulated emission depletion nanoscopy was used to confirm the internalization of the nanotubes in HeLa cells.