To provide an image-heating device having a flexible sleeve, capable of taking measures to cope with recording material whose size is slightly larger than regular size and reducing the rise time taken until a predetermined temperature is attained, after power is supplied.

The image heating device includes the flexible sleeve 21 having an elastic layer 21-2; a heating body 22 coming into contact with an inner peripheral surface of the flexible sleeve, and a pressure member 26 brought into contact with an outer peripheral surface of the flexible sleeve and forming a nip N, in cooperation with the heating body, and heats the recording material P carrying an image t while holding and conveying it in the nip, wherein the thermal conductivity λ of the elastic layer of the flexible sleeve is 1.0W/mk or more, the heat capacity Cp per unit length of the flexible sleeve is 60J/mK or less, and the heat capacity C of the entire flexible sleeve is 10J/K or more.