A drainage bag is provided for a thermal control unit adapted to deliver temperature-controlled liquid to a patient in order to control the patient's temperature. The drainage bag is used to hold and transport the liquid when the liquid inside the thermal control unit is changed. The drainage bag includes a bottom layer, a top layer sealed thereto, and a float secured to the top layer that is positioned adjacent an opening in the top layer. As the liquid from the thermal control unit drains into the opening in the top layer, the liquid lifts the float and the float lifts the top layer of the bag. The bag thereby expands its volume to accommodate the liquid from the thermal control unit. The bag may further be designed to be carried without sealing the opening and without spilling the liquid. A method for using the bag is also disclosed.