A sensor of volatile substances including: a sensitive layer, of a sensitive material that is permeable to a volatile substance and has an electrical permittivity depending upon a concentration of the volatile substance absorbed; a first electrode structure and a second electrode structure capacitively coupled together and arranged so that a capacitance between the first electrode structure and the second electrode structure is affected by the electrical permittivity of the sensitive material; and a supply device, configured to supply a heating current through one between the first electrode structure and the second electrode structure in a first operating condition, so as to heat the sensitive layer.