In this paper, we report opportunities to maximize the overall heat transfer rate of a cooler and reheater by appropriately shaping the flue gas desulfurization equipment of a thermal power plant driven by coal-firing combustion. The hottest combustion gas experiences a temperature drop through the cooler, which heats the water that circulates through the cooler and reheater. Constructal design is implemented in order to determine flow configurations that are superior. The overall heat transfer area is constrained (finite). We show that the most effective allocation of the heat transfer area can be pursued so that the maximum heat transfer density (or, compactness, as watts per volume) is achievable. The paper also documents two design candidates at the cooler outlet (with and without a maximum allowable gas stream temperature) and considers the balanced and unbalanced counter flows. The performance is superior when more degrees of freedom are allowed in the design. Copyright (c) 2015 John Wiley & Sons, Ltd.