Thermo-responsive triblock copolymers were synthesized by atom transfer radical polymerization of N-isopropyl acrylamide (NIPAAm) and N,N-dimethyl acrylamide (DMAAm) using α,ω-bromopropionyl poly(L-lactide) as the macro-initiator and a CuCl/tris(2-dimethylaminoethyl) amine (Me6TREN) complex as the catalyst. The polymerization was realized at 25 °C in a DMF–water mixture. DMAAm was incorporated in the copolymer as a hydrophilic comonomer in order to tune the lower critical solution temperature (LCST). The LCST linearly increases from 32.2 to 39.1 °C upon increasing the DMAAm content from 0 to 24%. The phase transition of polymeric micelles at the LCST occurs in a narrow temperature interval below 0.5 °C. Reversible size changes are observed when the temperature increases from 25 to 45 °C and then decreases down to 25 °C. Nano-size micelles (37 to 54 nm) with narrow distribution were obtained by self-assembly of amphiphilic copolymers in aqueous medium. The critical micelle concentration (CMC) ranges from 0.010 to 0.015 mg mL−1. In vitro drug release studies show a much faster release at temperatures above the LCST. The MTT assay was conducted to evaluate the cytotoxicity of copolymers. Therefore, the nano-scale size, low CMC, rapid phase transition, LCST slightly above body temperature and thermo-responsive drug release indicate that these copolymers could be potential candidates for applications in targeted delivery of drugs.