An effective chemotherapy for neoplastic diseases requires the use of drugs that can reach the site of action at a therapeutically efficacious concentration and maintain it at a constant level over a sufficient period of time with minimal side effects. Currently, conjugates of high-molecular-weight hydrophilic polymers or biocompatible nanoparticles with stimuli-releasable anticancer drugs are considered to be some of the most promising systems capable of fulfilling these criteria. In this work, conjugates of thermoresponsive diblock copolymers with the covalently bound cancerostatic drug pirarubicin (PIR) were synthesized as a reversible micelle-forming drug delivery system combining the benefits of the above-mentioned carriers. The diblock copolymer carriers were composed of hydrophilic poly[N-(2-hydroxypropyl)methacrylamide]-based block containing a small amount (∼ 5 mol %) of comonomer units with reactive hydrazide groups and a thermoresponsive poly[2-(2-methoxyethoxy)ethyl methacrylate] block. PIR was attached to the hydrophilic block of the copolymer through the pH-sensitive hydrazone bond designed to be stable in the bloodstream at pH 7.4 but to be degraded in an intratumoral/intracellular environment at pH 5-6. The temperature-induced conformation change of the thermoresponsive block (coil-globule transition), followed by self-assembly of the copolymer into a micellar structure, was controlled by the thermoresponsive block length and PIR content. The cytotoxicity and intracellular transport of the conjugates as well as the release of PIR from the conjugates inside the cells, followed by its accumulation in the cell nuclei, were evaluated in vitro using human colon adenocarcinoma (DLD-1) cell lines. It was demonstrated that the studied conjugates have a great potential to become efficacious in vivo pharmaceuticals.