A thermoresponsive, biocompatible and water soluble copolymer was synthetized via RAFT from 2-(2-methoxyethoxy)ethyl methacrylate (MEO2MA) and oligo (ethylene glycol) methacrylate (OEGMA) in the molar ratio of 9:1. The thermal behavior of the bulk material was investigated through thermogravimetric analysis and differential scanning calorimetry, revealing a fully amorphous polymer whose glass transition's onset is located at -47 °C. The molecular mobility was investigated below and above the glass transition temperature by dielectric relaxation spectroscopy and thermally stimulated depolarization currents, covering the frequency range from 10−3–106 Hz. Multiple relaxation processes were detected. The main process (α) is associated with the dynamical glass transition, whose temperature dependence of relaxation times exhibits the curvature in the relaxation map typical of cooperative processes, with a fragility index characteristic of strong materials. Moreover, two secondary relaxations, β and γ, were observed with Arrhenius temperature dependence of their relaxation times. The β-process show features compatible with a Johari-Goldstein process. Additionally, conductivity of pure dc origin was detected in the low frequency side of the α-relaxation. Its temperature dependence (logσdc vs. 1/T) also shows a curvature indicative of a coupling between charge transport and the segmental relaxation.