An apparatus for heating parenteral fluids for intravenous delivery to a patient. The apparatus includes a disposable cassette which in one presently preferred embodiment is made up of a unitary member which is divided to form a serpentine flow path by a plurality of path separators. Thin, flexible metallic foil membranes are sealingly joined to the unitary member on the upper and bottom surfaces thereof to form an enclosed, fluid-tight serpentine flow path between the plurality of path separators. The entire periphery of the unitary member and the thin, flexible heat conductive foil membranes are sealingly held by a framework. The disposable cassette slides between first and second heating blocks which contact the thin, flexible heat conductive foil membranes so as to provide heat transfer to fluid flowing in the serpentine flow path. The heating blocks are designed to provide a gradation of heat energy such that more heat energy is available for transfer to the parenteral fluid at the inlet end of the serpentine flow path than is available for transfer to the parenteral fluid at the outlet end of the serpentine flow path.