We study the thermal structure of the intra-cluster medium (ICM) in a set of cosmological hydrodynamical cluster simulations performed with an SPH numerical scheme employing an artificial conductivity (AC) term. We explore the effects of this term on the ICM temperature and entropy profiles, thermal distribution, velocity field and expected X-ray emission. We find that in adiabatic runs the artificial conductivity favours (i) the formation of an entropy core, raising and flattening the central entropy profiles, in better agreement with findings from Eulerian codes; and (ii) a systematic reduction of the cold gas component. In fact, the cluster large-scale structure and dynamical state are preserved across different runs, but the improved gas mixing enabled by the AC term strongly increases the stripping rate of gas from the cold clumps moving through the ICM. This in turn reduces the production of turbulence generated by the instabilities which develop because of the interaction between clumps and ambient ICM. We then find that turbulent motions, enhanced by the time-dependent artificial viscosity scheme we use, are rather damped by the AC term. The ICM synthetic X-ray emission substantially mirrors the changes in its thermo-dynamical structure, stressing the robustness of the AC impact. All these effects are softened by the introduction of radiative cooling but still present, especially a partial suppression of cold gas. Therefore, not only the physics accounted for, but also the numerical approach itself can have an impact in shaping the ICM thermo-dynamical structure and ultimately in the use of SPH cluster simulations for cosmological studies.