Star-shaped copolymers consisting of centrally located β-cyclodextrin and fifteen side chains containing di(ethylene glycol) methyl ether methacrylate (DEGMA) and poly(ethylene glycol) methyl ether methacrylate (OEGMA500) distributed statistically were synthesized using three different atom transfer radical polymerization (ATRP) techniques. For the first time, the use of β-cyclodextrin as a naturally-derived core for thermoresponsive polymeric drug delivery systems was thoroughly investigated depending on the chosen ATRP concept, focusing on precise control of the lower critical solution temperature (LCST) modulating the monomer content. The thermoresponsive properties of the received copolymers were investigated by UV–Vis and dynamic light scattering (DLS) measurement to determine the transmittance of solutions containing polymers with different monomer compositions and hydrodynamic diameter of prepared macromolecules upon temperature changes. The developed method allows for fine-tuning of the LCST by adjusting only the composition of the monomers. Synthesized copolymers were subsequently tested for residual copper catalyst content using atomic absorption spectrometry (AAS) to ensure compliance with the daily intake framework. The attained results showed negligible copper concentration in the purified products. Encouraged by these findings, cytotoxicity tests were conducted on normal fibroblast, cancer liver, and cancer breast cells, revealing no significant reduction in cell viability even at high polymer concentrations.