The lack of selectivity and low solubility of many chemotherapeutics impels the development of different biocompatible nanosized drug carriers. Amphiphilic block copolymers, composed of a hydrophilic and hydrophobic domain, show great potential because of their small size, large solubilizing power and loading capacity. In this paper, we introduce a new class of degradable temperature-responsive block copolymers based on the modification of N-(2-hydroxypropyl)methacrylamide (HPMA) with an ethyl group via a hydrolytically sensitive carbonate ester, polymerized by radical polymerization using a PEG-based macroinitiatior. The micellization and temperature-responsive behavior of the PEG-poly(HPMA-EC) block copolymer were investigated by dynamic light scattering (DLS). We observed that the polymer exhibits lower critical solution temperature (LCST) behavior and that above the cloud point (cp) of 17 °C the block copolymer self-assembles in micelles with a diameter of 40 nm. Flow cytometry analysis and confocal microscopy show a dose-dependent cellular uptake of the micelles loaded with a hydrophobic dye. The block copolymer nanoparticles were capable of delivering the hydrophobic payload into cancer cells in both 2D and 3D in vitro cultures. The block copolymer has excellent cytocompatibility, whereas loading the particles with the hydrophobic anticancer drug paclitaxel results in a dose-dependent decrease in cell viability.