By using free-radical RAFT living polymerization, we successfully grafted linear poly(N-isopropylacrylamide) (PNIPAM) chains onto a spherical PNIPAM/HEA copolymer microgel to form a novel core-shell nanostructure. Both the tethered PNIPAM shell and the copolymer microgel core shrunk as the temperature increased, but in different temperature ranges. In the range similar to28-32 degreesC, the tethered PNIPAM chains under-went a coil-to-globule transition, while in the range similar to32-35 degreesC, the shrinking of the copolymer core induced a re-stretching of the collapsed PNIAPM chains on its surface to form a polymer brush in poor solvent. Our results showed that in the re-stretching process, the average hydrodynamic volume per tethered PNIPAM chain remained a constant, confirming a prediction made a long time ago that the collapsed chains in poor solvent were incompressible.