Incorporating stimuli-responsive block copolymers to hierarchical metallic nanoparticles (MNPs) is of particular interest due to their tunable plasmonic properties responding to environmental stimuli. We herein report thermo-responsive plasmonic core-satellite hybrid nanostructures with tunable nanogaps as surface-enhanced Raman scattering (SERS) nanotags. Two different diblock copolymers with opposite charges, poly(acrylic acid-b-N-isopropylacrylamide) (p(AAc-b-NIPAM)) and poly(N,N-dimethylaminoethyl methacrylate-b-N-isopropylacrylamide) (p(DMAEMA-b-NIPAM)), were synthesized. The negatively charged p(AAc-b-NIPAM)s were bound to gold nanospheres (GNSs), while the positively charged p(DMAEMA-b-NIPAM)s were conjugated to gold nanorods (GNRs) via gold-sulfur bonds. When p(AAc-b-NIPAM)-GNSs and p(DMAEMA-b-NIPAM)-GNRs were electrostatically complexed, plasmonic hybrid nanostructures consisting of both GNS satellites and a GNR core were formed. Dynamic tuning of electromagnetic coupling of their nanogaps was achieved via a temperature-triggered conformational change of p(NIPAM) blocks. Furthermore, a sandwich-type immunoassay for the detection of immunoglobulin G was performed to demonstrate these core-satellites as potential SERS nanotags. Our results showed that these plasmonic core-satellites with stimuli-responsiveness are promising for SERS-based biosensing applications.