During the last decade, stimuli-responsible polymers based on poly(N-isopropylacrylamide) having conformational transition in the range of physiological temperature have been discussed as novel drug delivery nanosystems. A star-like copolymer with a dextran core and grafted poly(N-isopropylacrylamide) arms (D-g-PNIPAM) was synthesized, characterized, and used as a matrix for silver sol preparation. The comparative study of the behavior of individual D-g-PNIPAM and the nanohybrid system D-g-PNIPAM/silver nanoparticles has been done in the temperature range near the lower critical solution temperature (LCST). The methods of Dynamic Light Scattering, small angle X-ray scattering, and UV-VIS absorption spectroscopy have been used. The existence of single nanoparticles and aggregated nanoparticles located in a limited polymer macromolecular volume was established. The increase of the temperature leads to slight aggregation of the silver nanoparticles at the LCST transition. Single nanoparticles do not aggregate with the temperature increase. The thermally induced collapse of end-grafted poly(N-isopropylacrylamide) chains above the LCST do not affect significantly the size characteristics of silver nanoparticles incorporated into the polymer matrix.