We investigate the effect of block copolymer (BCP) molecular weight and connectivity on the morphology and time-temperature dependent swelling of thin film hydrogels created through layer-by-layer (LbL) assembly of BCP micelles with poly(acrylic acid). BCPs of poly(N,N-dimethylaminoethyl methacrylate) (I)) and poly(propylene oxide) (P), a P-D diblock, a long D-P-D triblock, and a short D-P-D triblock copolymer, were compared in terms of their temperature response in solution and within micelle-polyelectrolyte multilayers (mPEMs). The critical micellization concentration and micellization temperature of the BCPs in solution, as well as the swelling transition temperature, T-stt, of the mPEMs, decreased with increasing P block length. AFM imaging of dry mPEMs shows regular dimpled surface structures that arise from surface relaxation of micelles. When the mPEMs are cooled below T-stt in water, the thin similar to 200 nm films can swell reversibly between 3 and 6 times their dry thicknesses within 2 min. The degree, of swelling (tau = wet thickness/dry thickness) increases with undercooling (Delta T = T-stt - T) and shows time dependencies related to Delta T and the constituent BCP connectivity. While the diblock films swell uncontrollably and lose integrity within 30 min at Delta T >= 6 degrees C, the triblock copolymer multilayers are able to sustain steady tau values (in the range of 4-10) under equivalent conditions. The differences in dynamic swelling behavior originating from BCP architecture have important implications in their utility as temperature responsive surfaces.