The temperature dependence of electric transport properties of single-layer and few-layer graphene at large charge doping is of great interest both for the study of the scattering processes dominating the conductivity at different temperatures and in view of the theoretically predicted possibility to reach the superconducting state in such extreme conditions. Here we present the results obtained in 3-, 4- and 5-layer graphene devices down to 3.5 K, where a large surface charge density up to about 6.8·10(14) cm(-2) has been reached by employing a novel polymer electrolyte solution for the electrochemical gating. In contrast with recent results obtained in single-layer graphene, the temperature dependence of the sheet resistance between 20 K and 280 K shows a low-temperature dominance of a T(2) component - that can be associated with electron-electron scattering - and, at about 100 K, a crossover to the classic electron-phonon regime. Unexpectedly, this crossover does not show any dependence on the induced charge density, i.e. on the large tuning of the Fermi energy.