In offline comparisons to the numerical solution for reservoir heat depletion (see Sec. 2.4), we found that it is best to use the area-based equivalent radius outside of 𝜖 (i.e., in Equations 29 and 31). This ensures that the temperature is correct as the time approaches infinity because the late-time steady state temperature occurs when the heat extraction rate is equal to the rate of conductive heat flow into the reservoir. We use the volume-based radius within the calculation of 𝜖 (Equation ), which gives the reservoir the right initial amount of heat.