Pick a scenario; every slider below stays editable.
Curve: heat loss now. Flat lines: resting metabolism and the shivering ceiling. Where the curve crosses a line is the lower critical temperature or the survival limit.
Gold: air temperature (left axis). Green: core body temperature (right axis, 30 to 40 C).
The science
Model. The animal is a cylinder of radius r1 and effective length l = 1.7 (m/40 kg)1/3 m (this lumps legs, head and tail into one equivalent area of about 1.1 m² for 40 kg, close to Meeh's 0.1 m2/3) covered by a fur layer of thickness t. Skin sits at core temperature minus 2.5 K.
Conduction through fur (per metre of length): q' = 2π keff (Tskin - Ts) / ln(r2/r1), with k = 0.045 W/m/K for dense still-air fur (typical value; trapped air dominates). Wind pushes air into the coat: keff = k (1 + 0.06 v) — the 0.06 s/m is an illustrative coefficient, not a measurement.
Outside the fur. Surface temperature Ts comes from the balance q' = πD [ h (Ts - Ta) + εσ(Ts4 - Tsky4) ] (bisection, D = 2 r2). Convection: Churchill-Bernstein forced flow across a cylinder, Nu = 0.3 + 0.62 Re1/2 Pr1/3 / [1+(0.4/Pr)2/3]1/4 [1+(Re/282000)5/8]4/5, blended with Churchill-Chu natural convection for calm air (cube-root blend). Air viscosity scales with 1/pressure, so thin mountain air (62 kPa at 4000 m) conducts the same but carries less momentum: Reynolds number drops. Radiation to a clear sky 18 K colder than the air (5 K when cloudy; the shelter sees air temperature), ε = 0.95.
Metabolism. Kleiber's law BMR = 3.39 m0.75 W (70 kcal/day per kg0.75); resting Mrest = 1.5 BMR, maximal sustained shivering Mmax = 4 BMR (both typical textbook multipliers, not species measurements). Idealised thermoregulation: M = clamp(Q + 40 (37.5 - Tcore), Mrest, Mmax). Core temperature follows m c dT/dt = M - Q with c = 3470 J/kg/K. Below about 35 C the animal is hypothermic. Extra food is converted with an assumed 6 MJ per kg of fresh meat.
Posture. Lying reduces the exposed area to 80 % and curling with the tail over the nose to 55 % (illustrative factors in the spirit of the published curl-up savings; real values vary). The shelter cuts the wind to 12 % and removes sky radiation loss.
Lower critical temperature is the air temperature where heat loss equals resting metabolism; the leopard wind chill is the calm-air temperature that would give the same heat loss, so it is specific to this coat and body, not the human wind-chill index.
Honest simplifications. One lumped cylinder (no paws, ears or face, which in reality lose proportionally more); no snow contact conduction, no water or ice in the fur, no panting, no behaviour other than posture; the thermal-view colours of ears, face and paws are illustrative offsets, not calculated. Coat thickness and conductivity are typical figures and the animal can actually grow 5 cm or more of belly fur. Model and picture are educational; nothing here is veterinary advice.