A patient temperature control system comprising: a) a fluid circuit for conveying warming/cooling fluid to a patient warming/cooling device applied to a patient for hypo-hyperthermia treatment; b) a controller operatively connected to the fluid circuit to control the flow and the temperature of the warming/cooling fluid therethrough; c) a first temperature sensor adapted to sense the temperature of the patient and operatively connected to the controller; d) a second temperature sensor adapted to sense the temperature of the warming/cooling fluid and operatively connected to the controller; e) the controller adapted to warm the warming/cooling fluid being conveyed to the warming/cooling device, thereby to warm the patient when the first sensor senses a patient temperature lower than a selected target temperature; f) the controller also operative to cool the warming/cooling fluid being conveyed to the warming/cooling device, thereby to cool the patient when the first sensor senses a patient temperature higher than the selected target temperature; g) wherein the controller automatically controls the warming or cooling of the warming/cooling fluid during an initial stage, at a temperature that differs from the sensed patient temperature by, at a maximum, a predetermined initial stage temperature gradient; and h) the controller, during a subsequent stage, automatically controls the warming or cooling of the warming/cooling fluid by automatically varying the magnitude of the temperature gradient from the predetermined initial stage temperature gradient toward a subsequent temperature gradient, in response to a subsequently sensed temperature of the patient as sensed via the first sensor, if the sensed patient temperature has not moved sufficiently close to the selected target temperature, thereby to more quickly bring the temperature of the patient to the selected target temperature and to do so in a manner which minimizes overshoot, i) wherein the controller causes the subsequent variations in the magnitude of the temperature gradient to occur at specified time intervals, and j) wherein the controller causes an incremental increase or decrease of the subsequent temperature gradient after each specified time interval if the sensed patient temperature has not moved sufficiently in the previous specified time interval. a) a fluid circuit for conveying warming/cooling fluid to a patient warming/cooling device applied to a patient for hypo-hyperthermia treatment; b) a controller operatively connected to the fluid circuit to control the flow and the temperature of the warming/cooling fluid therethrough; c) a first temperature sensor adapted to sense the temperature of the patient and operatively connected to the controller; d) a second temperature sensor adapted to sense the temperature of the warming/cooling fluid and operatively connected to the controller; e) the controller adapted to warm the warming/cooling fluid being conveyed to the warming/cooling device, thereby to warm the patient when the first sensor senses a patient temperature lower than a selected target temperature; f) the controller also operative to cool the warming/cooling fluid being conveyed to the warming/cooling device, thereby to cool the patient when the first sensor senses a patient temperature higher than the selected target temperature; g) wherein the controller automatically controls the warming or cooling of the warming/cooling fluid during an initial stage, at a temperature that differs from the sensed patient temperature by, at a maximum, a predetermined initial stage temperature gradient; and h) the controller, during a subsequent stage, automatically controls the warming or cooling of the warming/cooling fluid by automatically varying the magnitude of the temperature gradient from the predetermined initial stage temperature gradient toward a subsequent temperature gradient, in response to a subsequently sensed temperature of the patient as sensed via the first sensor, if the sensed patient temperature has not moved sufficiently close to the selected target temperature, thereby to more quickly bring the temperature of the patient to the selected target temperature and to do so in a manner which minimizes overshoot, i) wherein the controller causes the subsequent variations in the magnitude of the temperature gradient to occur at specified time intervals, and j) wherein the controller causes an incremental increase or decrease of the subsequent temperature gradient after each specified time interval if the sensed patient temperature has not moved sufficiently in the previous specified time interval.