An applicator for a fluid product offers a thermal effect by creating a cold sensation upon application to a surface. The applicator comprises a reservoir containing a fluid product; an end-piece with a dispensing face having an orifice for dispensing the fluid product onto the surface to be treated; and a thermal storage end-piece that includes an application face. The thermal storage end-piece is made from a material having a thermal effusivity that is higher than that of the product dispensing end-piece so as to provide thermal sensations upon contact with the surface to be treated. The application head is shaped so that, by orienting the applicator selectively relative to the surface to be treated, one can place the latter in contact with the dispensing face of the dispensing end-piece while avoiding contact with the application face of the thermal storage end-piece.