The body's core temperature obeys a one-node heat-balance equation. Heat storage S (W/m² of skin) drives the rate of change:
S = M − E − C
dTcore/dt = S · A_body / (mass · c_body)
M = metabolic heat production (W/m²)
E = actual evaporative heat loss (W/m²)
C = dry (convective) heat exchange with air (W/m²)
A_body ≈ 1.8 m², mass ≈ 70 kg, c_body ≈ 3492 J/(kg·°C)
Evaporation is capped by how much moisture the surrounding air can actually absorb — not by how much you sweat. That cap, E_max, comes straight from psychrometrics (Tetens' formula for saturation vapour pressure, and the Lewis relation linking convective and evaporative transfer coefficients):
P_sat(T) = 0.6108 · exp(17.27·T / (T+237.3)) [kPa]
h_c = 8.3 · wind^0.6 (convective coeff.)
h_e = 16.5 · h_c (Lewis relation)
E_max = h_e · [ P_sat(T_skin) − RH·P_sat(T_air) ]
E = min( sweat demand , E_max )
- Air temperature / humidity / wind — set the environment. Humidity shrinks the vapour-pressure gap in E_max even when the skin is soaked, which is why sweating stops working long before the air itself feels "hot" — this is the physical basis of the wet-bulb temperature danger threshold (≈35°C WBT is considered the theoretical limit of survivable heat exposure for a healthy resting adult, Sherwood & Huber, 2010).
- Activity level — sets metabolic heat production M, from resting (~65 W/m²) to heavy labour (~300 W/m²): more internal heat that still has to leave the body through the same evaporative bottleneck.
- Droplets on the body — visualise the sweat response. When E_max is high (dry, breezy air) droplets flash-evaporate and shrink away quickly — effective cooling. When E_max is low (humid, still air) droplets linger and drip uselessly down the skin: sweat production without heat loss, exactly the mechanism behind heat-exhaustion and heat-stroke mortality during real urban heatwaves.
- Skin flushing (redness) shows cutaneous vasodilation — blood flow to the skin rises as core temperature climbs, in an attempt to shed more heat by convection.