Excursion-sets of the gas temperature for the fiducial model at z = 5 for different values of the threshold: whole field (top left), T ≥ 6 × 10³ K (top middle), T ≥ 8 × 10³ K (top right), T ≥ 1 × 10⁴ K (bottom left), T ≥ 3 × 10⁴ K (bottom middle) and T ≥ 5 × 10⁴ K (bottom right). For illustrative purposes, 3D maps correspond to fields before applying additional Gaussian smoothing of 1.56 h⁻¹ Mpc. Low values of the threshold reveal cold isolated cavities, at intermediate thresholds an interconnected filamentary structure emerges, while higher thresholds delimit hot regions forming isolated clumps. The Minkowski functionals computed for these thresholded 3D maps quantify the complex morphology of the underlying temperature field. See Figure 3 for analogous excursion-sets at z = 0.