Drugs can be delivered by a temperature change-driven shrinking of the nanocarrier followed by the cargo release. This paper describes a different structural response to temperature, performed by nanoparticles of poly(N-isopropylacrylamide) and hyaluronic acid. Around 35 °C, the hydrophobicity of the vinyl polymer drives a core-shell rearrangement with the acrylamide chains confined in the core and the polysaccharide moiety forming the shell. In this arrangement, the nanoparticles enable the active targeting of tumor cells, due to the specific interaction of hyaluronic acid with the CD44 receptors. When doxorubicin-loaded nanoparticles are up-taken, the polysaccharide part degrades in the cytoplasm and the cytotoxic effect of the anticancer drug in colon adenocarcinoma cells has a 2-fold increase with respect to healthy fibroblasts. These core-shell particles have hyaluronic acid as the key factor for the specific targeting of tumor cells and drug release with poly(N-isopropylacrylamide) driving the transition.