A blood warming device circulates air as a heating medium through a heater element and heat exchangers to transfer heat from the air to chilled blood being forced through the channels in a disposable warming jacket. A temperature sensor is disposed near an outlet of the blood warming jacket. An electronic control circuit operates on the signals produced by the temperature sensor to produce a cutoff signal that immediately stops the flow of heated air through the heat exchanger if the sensed blood temperature exceeds a predetermined level. The low heat capacity of the air is sufficiently low that no overheating of blood in the blood warming jacket occurs even if the blood flow is interrupted so that blood remains stationary in the blood warming jacket. The disposable warming jacket inclues a plurality of parallel blood paths, resulting in a high flow rate of heated blood. Blood output from one section of a warming jacket can be input to the inlet of another section to further raise the temperature thereof.