Water-soluble amphiphilic random copolymers composed of tri(ethylene glycol) methacrylate (TEGMA) or poly(ethylene glycol) methyl ether methacrylate (PEGMA) and perfluorohexylethyl acrylate (FA) were synthesized by ARGET-ATRP, and their self-assembling and thermoresponsive behavior in water was studied by dynamic light scattering (DLS) and UV-vis spectroscopy. The copolymer ability to self-fold in single-chain nano-sized structures (unimer micelles) in aqueous solutions was exploited to encapsulate Combretastatin A-4 (CA-4), which is a very hydrophobic anticancer drug. The cloud point temperature (Tcp) was found to linearly decrease with increasing drug concentration in the drug/copolymer system. Moreover, while CA-4 was preferentially incorporated into the unimer micelles of TEGMA-ran-FA, the drug was found to induce multi-chain, submicro-sized aggregation of PEGMA-ran-FA. Anyway, the encapsulation efficiency was very high (≥81%) for both copolymers. The drug release was evaluated in PBS aqueous solutions both below and above Tcp for TEGMA-ran-FA copolymer and below Tcp, but at two different drug loadings, for PEGMA-ran-FA copolymer. In any case, the release kinetics presented similar profiles, characterized by linear trends up to ≈10–13 h and ≈7 h for TEGMA-ran-FA and PEGMA-ran-FA, respectively. Then, the release rate decreased, reaching a plateau. The release from TEGMA-ran-FA was moderately faster above Tcp than below Tcp, suggesting that copolymer thermoresponsiveness increased the release rate, which occurred anyway by diffusion below Tcp. Cytotoxicity tests were carried out on copolymer solutions in a wide concentration range (5–60 mg/mL) at 37 °C by using Balb/3T3 clone A31 cells. Interestingly, it was found that the concentration-dependent micro-sized aggregation of the amphiphilic random copolymers above Tcp caused a sort of “cellular asphyxiation” with a loss of cell viability clearly visible for TEGMA-ran-FA solutions (Tcp below 37 °C) with higher copolymer concentrations. On the other hand, cells in contact with the analogous PEGMA-ran-FA (Tcp above 37 °C) presented a very good viability (≥75%) with respect to the control at any given concentration.