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The science
Heat balance. Each quokka is one lumped body of heat capacity C = m c = 3 kg x 3470 J/kg/K: C dTb/dt = M + Pth + Qsun + G (Ta - Tb) - Pevap. Metabolic heat M = BMR x activity (BMR about 5.4 W for 3 kg, about 70 % of the eutherian Kleiber value), G is the whole-fur dry conductance (0.47 W/K, so the thermal time constant C/G is about 6 h), and shivering Pth adds up to 12 W when cold.
Sun and shade. Absorbed solar load Qsun = a A S sin(h) f (1 - shade) with fur absorptivity a = 0.7, projected area A = 0.08 m², clear-sky flux S = 900 W/m², and a factor f = 0.2 for the share that reaches the skin. Solar elevation sin h = sin φ sin δ + cos φ cos δ cos H (latitude 32° S, season sets the declination δ).
Evaporative cooling costs water. Licking and panting remove Pevap = min(Pmax, k (Tb - 36.8)) plus 1.2 W of respiratory loss; each watt-hour costs 3600 / Lv = 1.48 g of water (Lv = 2.43 MJ/kg). When the drinking reserve runs out the cooling capacity falls to 3 W. Water comes back from seeps (600 g/h) and from moist leaves (25 g/h while grazing).
Behaviour rules (a simple agent model, not data): hot or in sun at midday - walk to the nearest shade and rest; reserve low - walk to the nearest seep; otherwise forage. Quokkas are mostly nocturnal, and the rules reproduce that: they rest in shade by day and forage after dusk.
Honest simplifications. One-compartment body at one temperature; no behavioural posture changes, burrows, wind chill on wet fur or humidity; solar load is a lumped factor, not a radiative transfer model; the island, shrubs and seeps are a stylised map, not Rottnest Island. Every constant is a typical illustrative value for a 3 kg marsupial, not a measurement; the heat-stress limit of 39 C is a round number. Quokkas are a protected species: this is an educational model and never a guide to handling wildlife.