A vehicle provided with an engine, at least one air intake through which the engine takes in the external air needed to operate, and an air filter arranged downstream of the air intake. The air filter presents: at least one filtering material panel having a corrugated shape having a plurality of crests disposed towards an outer environment and a plurality of valleys arranged towards an internal environment; an outer reinforcement mesh; an inner reinforcement mesh; and a heating device which is designed to heat the filtering material panel. The heating device presents: a plurality of electrical conductors, which are completely independent and separated from the outer reinforcement mesh, rest on the outer surface of the filtering material panel, and are arranged only and exclusively at the crests; and a supply device designed to cause an electric current to flow through the electric conductors so as to generate heat, due to the Joule effect.