A disposable, in-line heating cassette and apparatus for raising the temperature of fluids. The cassette comprises a spacer defining a sinuous or serpentine flow pathway interposed between flexible foils and mounted on a frame. The frame comprises inlet and outlet tubes and related input and output ports which communicate with the serpentine path. Juxtaposed heating plates in direct contact with the cassette substantially contact the entire heating surface of the foils, providing a highly efficient thermal path from the heating plate to the foil, and then to the fluid. The heating blocks have several electrically conductive strips thereon for generating a gradation of heat energy such that more heat energy is available for transfer at the inlet end than the outlet end of the serpentine flow path. The strips are arranged on the heating plates immediately over and under the serpentine flow path and are divided into contiguous perpendicular sections, each section having a corresponding closest parallel section with a conductor separation distance therebetween.