This page gives details of the mathematical model of the heat generated and lost while running.

1 Basic Heat Calculation

The basic heat calculation is from

Heat produced from running. This is dependent mainly on your weight.
Heat lost (or gained) from convection. This is mostly dependent on your surface area (calculated from weight and height), and the air temperature.
Heat lost (or gained) from radiation. This is mostly dependent on your surface area and the air temperature.
Heat lost from evaporation of sweat. This is mostly dependent on your surface area, the air temperature and humidity.

2 Important caveats

These calculations make lots of assumptions.

Your running efficiency may be different to the average. A higher efficiency will produce less heat at a given pace, a lower efficiency will produce more heat.
The only air movement is assumed to be from running through still air.
- Any wind can make a significant difference, with a headwind or crosswind cooling your off. A tailwind less than twice your running pace will reduce your cooling; it takes a tailwind of at least twice your running pace to cool you off more than still air, but of course a tailwind will reduce the energy required to run.
The calculations assume negligible clothing. If you are wearing more than the absolute minimum clothing, this will impair your ability to cool off.
It is possible to actively cool off with ice, which will allow you to tolerate higher temperatures.
Any direct sun will increase the heat stress and dark clothing will make this worse.

These notes are for those with an interest in the underlying details.

There are multiple formulas for calculating water vapor pressure which produce slightly different results.
The calculation of skin temperature is not straightforward. The calculator uses a combination of Neilson's approach and the Mehnert formula.
The various formulas for calculating the surface area of the skin appear to give similar results.