Context. Strong theoretical and observational support exists that the spectral evolution of neutron-star LMXBs, including transient hard X-ray tails, can be explained by the interplay between thermal and bulk motion Comptonization. The introduction of a new XSPEC Comptonization model, Comptb, including thermal and bulk Comptonization, has provided additional support to this interpretation. Aims. We used Comptb to investigate the spectral evolution of the neutron-star LMXB Cyg X-2 along its Z track. We selected a single source to trace in a quantitative way the evolution of the physical parameters of the model. Methods. We analyzed archival broad-band BeppoSAX spectra of Cyg X-2. Five broad-band spectra were newly extracted by using information about the source position in the Z track described in the colour-colour and colour-intensity diagrams. Results. We fitted the spectra of the source with two Comptb components. The first one, with a bulk parameter δ = 0, represents the dominant component of the overall source broad-band spectrum and its origin is related to thermal upscattering (Comptonization) of cold seed photons by warm electrons in a high opacity enviroment. We attribute the origin of these seed photons to the section of the disk that illuminates the outer coronal region (transition layer) located between the accretion disk itself and the neutron-star surface. The physical properties of this thermal component are roughly constant with both time and inferred mass accretion rate. The second Comptb model describes the overall Comptonization (thermal plus bulk, δ > 0) of hotter seed photons that originate in both the inner transition layer and at the neutron-star surface. This component is more significant in the horizontal branch of the colour-colour or hardness-intensity diagram and progressively disappears towards the normal branch, where a pure blackbody spectrum is observed. Conclusions. The spectral evolution of Cyg X-2 is studied and interpreted in terms of changes in the innermost environmental conditions of the system, leading to a variable thermal-bulk Comptonization efficiency.