The parameters of proton beams accelerated by a high-intensity short pulse laser from a thin foil are studied for various small plasma gradients created on the rear-surface of the foil. Compared to the case of an initially cold foil, the proton beam maximum energy as well as the beam spectral slope reduce steadily when increasing the gradient scale length. The measurements are in good agreement with simulations. For future ion-driven Fast Ignition of fusion targets, multi-kJ Peta Watt laser pulses will induce target preheat due to the leading part of the laser pulse. Estimates of such preheat in these conditions suggest that it should modify by less than 10 % the ion beam parameters compared to the case of a unheated target.