A quick calculation shows that the maximum possible IV fluid flow rate with two 100W heaters (at 85% heat transfer efficiency) is approximately 80mL/min. This assumes that the blood product enters at 4degC (typical whole blood and packaged red blood cell storage temperature) and leaves at 39degC. 

Assuming the electronics consume an additional 12W of power, I arrive at a duration between battery charges of approximately 1 hour for a typical 12V, 45Ah car battery at a 17.7A discharge rate (based on the lead acid battery voltage curves I found online). At 80 mL/min, it is theoretically possible to warm thirteen 350mL units of blood product before the battery needs to be recharged.