A cooling system is provided which includes, for instance, a coolant circulation loop, one or more primary coolant pumps, and a fill and drain pump. The primary coolant pump(s) is coupled to facilitate circulating coolant through the coolant circulation loop, and the fill and drain pump facilitates selective filling of the cooling system with the coolant, or draining of the coolant from the cooling system. The fill and drain pump is integrated with the cooling system as a backup coolant pump to the primary coolant pump(s), and circulates the coolant through the coolant circulation loop responsive to an error in the primary coolant pump(s). The primary coolant pump(s) and fill and drain pumps may be different types of pumps, and the cooling system further includes a control system for automatically activating the fill and drain pump upon detection of an error in the primary coolant pump(s).