According to the invention, the cartridge (1) includes a thermostatic element (72) which is thermally activated by a mixture of a cold fluid and a hot fluid, which is mechanically connected to a regulator slide (70) and which is moved by a single lever (50) for controlling the flow rate and the temperature of said mixture. In order to improve cartridge temperature regulation within a large flow range, the cartridge includes second (30) and third discs (40) in addition to a first disc which is stationary relative to the cartridge body (10). The second disc is translationally stationary relative to the first disc and is capable of rotation under the action of the lever actuation via a nut partially containing a thermostatic-member-moving assembly (76, 78, 80) which is rotatably connected to the control lever about the axis (X-X) and which is provided with extensions (66) that engage mechanically with the second disc for rotating same. The third disc is rotatably connected to the second disc and is capable of translation under the action of the lever actuation. The third disc defines: (a) a cold fluid passage (41A) designed to establish a communication between an inlet (21A) and a return line (22A) for cold fluid, formed through the first disc via an inlet (31A) and a return line (32A) for cold fluid extending through the second disc in order to enable a high flow rate; and (b) a hot fluid passage (41B) designed to establish a communication between an inlet (21B) and a return line (22B) for hot fluid, formed through the first disc via a hot fluid inlet (31b) and a return line (32B) also extending through the second disc in order to enable a high flow rate.