A vulcanizable rubber composition is described comprising a cross-linkable unsaturated chain polymeric base, wherein is incorporated at least one organic compound, solid at room temperature, selected from the group comprising: amorphous or semicrystalline polymers, oligomers, low-molecular weight organic substances and mixtures thereof, which compound is substantially insoluble in the polymeric base and shows a first or second order transition temperature of from 80 to 160° C. Such rubber composition allows the manufacture of treads with either a low rolling resistance at the temperature of normal use of the tire (40°-70° C.), or a high grip when the tread is subjected to thermal stresses exceeding such temperatures.