Stimuli-responsive polymers are of crucial importance in the design of smart biomaterials. The thermo-responsive triblock copolymers of polycaprolactone (PCL) and poly(N-isopropylacrylamide) (P(NIPAAm)), or P(NIPAAm)b-PCL-b- P(NIPAAm) copolymers, were synthesized in this work via atom transfer radical polymerization (ATRP). The P(NIPAAm)-b-PCL-b-P(NIPAAm) copolymers were cast by phase inversion in water into porous membranes with well-defined and uniformly distributed pores. The P(NIPAAm) content in the P(NIPAAm)-b-PCL-bP(NIPAAm) copolymers and the temperature of the aqueous medium for phase inversion could be used to control the pore size and porosity of the membranes. The thermo-responsive characteristics of the membranes were illustrated in the controlled water uptake and temperature-dependent glucose transport through the membranes. These temperature-sensitive membranes with controllable morphology have potential applications in biomedical engineering, drug delivery, and tissue engineering.