Water-soluble, thermoresponsive block copolymers based on a biodegradable platform were synthesized by the ring opening polymerization of cyclic carbonate monomers functionalized with hydrophilic and hydrophobic groups for application as nanocarriers in medicine. The approach based on cyclic carbonate monomers derived from 2,2-bis(methylol)propionic acid (bis-MPA) allowed a simple and versatile route to functional monomers capable of undergoing ring opening polymerization (ROP). The resulting polymers possessed the predicted molecular weights based on the molar ratio between monomers to initiators and the narrow molecular weight distributions. Transmittance measurement for aqueous polymer solutions provided an evidence for temperature-responsiveness with lower critical solution temperature (LCST) in the range of 36 °C-60 °C, depending on the molecular weight of hydrophilic poly(ethylene glycol) (PEG) chains, compositions of copolymers, molar ratios of hydrophilic to hydrophobic monomers in the corona, and the hydrophobic core. This study showed synthetic advancement toward the design and preparation of biodegradable thermoresponsive polymers with extremely low CMC values for injectable drug delivery systems. TRC350-10,30,60, which possessed an LCST of 36 °C in PBS, was identified as a useful model polymer. Paclitaxel, an anti-cancer drug, was loaded into the micelles efficiently, giving rise to nano-sized particles with a narrow size distribution. Paclitaxel release from the micelles was faster, and cellular uptake of the micelles was higher at the body temperature (i.e. 37 °C) as compared to a temperature below the LCST. While the polymer was not cytotoxic, paclitaxel-loaded micelles killed HepG2 human liver carcinoma cells more efficiently at the body temperature as compared to free paclitaxel and paclitaxel-loaded micelles at the temperature below the LCST. These micelles are ideally suited to deliver anti-cancer drugs to tumor tissues through local injection.