Herein, we report the formation of drug delivery systems from original thermoresponsive block copolymers containing lipid-based segments. Two acrylate monomers derived from palmitic- or oleic-acid-based diacylglycerols (DAGs) were synthesized and polymerized by the reversible addition-fragmentation chain transfer (RAFT) method. Well-defined DAG-based polymers with targeted molar masses and narrow molar mass distributions were next used as macro-chain transfer agents (macro-CTAs) for the polymerization of N-isopropylacrylamide (NIPAAm) or N-vinylcaprolactam (NVCL). The obtained amphiphilic block copolymers were formed into polymeric nanoparticles (PNPs) with and without encapsulated doxorubicin and characterized. Their biological assessment indicated appropriate cytocompatibility with the representatives of normal cells. Furthermore, compared to the free drug, increased cytotoxicity and apoptosis or necrosis induction in breast cancer cells was documented, including a highly aggressive and invasive triple-negative MDA-MB-231 cell line.