The present invention is directed to a computer controlled apparatus for perfusing, cooling, and warming a biological organ. The apparatus includes a programmable computer, selectively addressable arterial perfusate reservoirs having inputs and outputs in a recirculating fluid flow path, a main pump in the recirculating flow path for recirculating the fluid in said path, an organ pump that withdraws fluid from the recirculating fluid flow path and provides it to one or more organs in an organ flow path for subsequent return to the recirculating fluid flow path or discard, a temperature-controlled cabinet housing most components of the apparatus, and improvements that permit organ perfusion at temperatures below -10.degree. C., immersion cooling of the organ to allow organ temperature reduction to below -40.degree. C. to -140.degree. C., immersion warming of the organ, and elimination of stagnant fluid in the organ flow path by means of an organ bypass valve. The apparatus may be simplified to be used exclusively for cooling on the one hand or for warming on the other. Cooling is normally accompanied by the introduction of cryoprotective agents at sub-zero temperatures, and warming is normally accompanied by the partial or complete removal of these agents.