Proteinlike copolymers were first predicted by the computer-aided biomimetic design (Physica A 1998, 249, 253-261). These copolymers consist of comonomer units of differing hydrophilicity/hydrophobicity. Heterogeneous blockiness, characteristic for such copolymers, facilitates chain folding with the formation of specific spatial packing: a dense core consisting of hydrophobic units and a polar shell formed by hydrophilic units. This paper describes the synthesis of N-vinylcaprolactam/N-vinylimidazole copolymers via the redox-initiated radical copolymerization in the medium of 10% aqueous DMSO at the temperatures both below and above the phase separation threshold. The synthesized macromolecular products were separated into thermally precipitating and nonprecipitating fractions. Their molecular weight characteristics were evaluated using size-exclusion chromatography; their comonomer composition was determined from 1H NMR spectra of copolymers dissolved in DMSO-d6. The temperature-dependent behavior of copolymer macromolecules in water was investigated by thermonephelometry, high-sensitivity differential scanning calorimetry, and 1H NMR spectroscopy of the copolymers dissolved in D2O. It was shown that thermally nonprecipitating copolymer fractions obtained at initial comonomer molar ratios of 85:15 and 90:10 can be identified as proteinlike copolymers.