Four series of poly(N-isopropylacrylamide) (PNIPAM) (core)/poly(N-isopropylacrylamide-co-3-acrylamidophenylboronic acid) (P(NIPAM-AAPBA)) (shell) microgels were synthesized by the modification of PNIPAM (core)/poly(N-isopropylacrylamide-co-acrylic acid) (P(NIPAM-AA)) (shell) microgels with 3-aminophenylboronic acid (APBA). Their thermosensitive behaviors were studied by dynamic light scattering. Two or three phase transitions were detected depending on the shell thickness. These transitions were confirmed by the first derivative plot of the turbidity data. The first transition occurring at about 17 degrees C was assigned to that of the P(NIPAM-AAPBA) shell, whereas the second and third ones, which occur at about 22 and 28 degrees C, respectively, were assigned to that of the PNIPAM core. These results indicate that the influences of a shrunk P(NIPAM-AAPBA) shell on the different parts of the PNIPAM core are different. As the outer part, or the "shell" part of the PNIPAM core, directly connects with the P(NIPAM-AAPBA) shell, its phase transition temperature is reduced to a larger degree as compared with that of the inner part, or the "core" part. Glucose-induced swelling was observed for all the microgels, indicating their glucose-sensitivity. However, the degree of glucose-induced swelling is much smaller than that of the pure P(NIPAM-AAPBA) microgels.