A glossing device for processing a toner image on a recording medium, the device comprising: a heater member subjected to heating; a stripper member parallel to the heater member; an endless rotary belt looped for rotation around the heater member and the stripper member in a longitudinal, conveyance direction of the belt; a pressure member opposite the heater member via the belt; the heater member and the pressure member pressing against each other via the belt to form a glossing nip (Ng) therebetween through which the recording medium is conveyed under heat and pressure, the recording medium after passage through the nip (Ng) remaining in contact with the belt as the belt moves from the heater member toward the stripper member, and separating from the belt as the belt passes around the stripper member; and a belt cooler adjacent to the belt to cool the belt downstream from the heater member and upstream from the stripper member, the glossing device characterized in that the belt cooler includes: a pair of separate, first and second cooling elements (40U, 40D) inside the loop of the belt, the former being closer than the latter to the heater member in the conveyance direction of the belt, to establish thermal contact with the belt, wherein an area of thermal contact between the first cooling element and the belt is larger than an area of thermal contact between the second cooling element and the belt; a pair of first and second heat dissipators (50U, 50D) connected to the first and second cooling elements (40U, 40D), respectively, to dissipate heat from the cooling element (40U, 40D), wherein the first heat dissipator exhibits a higher cooling capacity of dissipating heat per unit of time than the second heat dissipator. a heater member subjected to heating; a stripper member parallel to the heater member; an endless rotary belt looped for rotation around the heater member and the stripper member in a longitudinal, conveyance direction of the belt; a pressure member opposite the heater member via the belt; the heater member and the pressure member pressing against each other via the belt to form a glossing nip (Ng) therebetween through which the recording medium is conveyed under heat and pressure, the recording medium after passage through the nip (Ng) remaining in contact with the belt as the belt moves from the heater member toward the stripper member, and separating from the belt as the belt passes around the stripper member; and a belt cooler adjacent to the belt to cool the belt downstream from the heater member and upstream from the stripper member, the glossing device characterized in that the belt cooler includes: a pair of separate, first and second cooling elements (40U, 40D) inside the loop of the belt, the former being closer than the latter to the heater member in the conveyance direction of the belt, to establish thermal contact with the belt, wherein an area of thermal contact between the first cooling element and the belt is larger than an area of thermal contact between the second cooling element and the belt; a pair of first and second heat dissipators (50U, 50D) connected to the first and second cooling elements (40U, 40D), respectively, to dissipate heat from the cooling element (40U, 40D), wherein the first heat dissipator exhibits a higher cooling capacity of dissipating heat per unit of time than the second heat dissipator. a pair of separate, first and second cooling elements (40U, 40D) inside the loop of the belt, the former being closer than the latter to the heater member in the conveyance direction of the belt, to establish thermal contact with the belt, wherein an area of thermal contact between the first cooling element and the belt is larger than an area of thermal contact between the second cooling element and the belt; a pair of first and second heat dissipators (50U, 50D) connected to the first and second cooling elements (40U, 40D), respectively, to dissipate heat from the cooling element (40U, 40D), wherein the first heat dissipator exhibits a higher cooling capacity of dissipating heat per unit of time than the second heat dissipator.