Hi William, 

A good history section is in the attached paper. Although the review in general is related to cold exposure modelling it covers a lot of thermoregulatory modelling in general (in the brief history section). 

It largely depends on what equation you want to reference, they range from very simple to very complex (when accounting for local blood flow, shivering etc). I hope this helps in some way. 

Not sure if it is the original source, but Gates (1980) Biophysical ecology (book) is what we typically cite as a reference for heat-budget modeling.  That might be a place to start.

The background of all the modern thermal physiology of endothermic animals is the set of papers by Scholander et al. published in 1950:

Scholander, P. F.; Hock, R.; Walters, V. & Irving, L. Adaptation to cold in arctic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate. Biol. Bull., 1950, 99(2): 259-271.

Scholander, P. F.; Hock, R.; Walters, V.; Jonson, F. & Irving, L. Heat regulation in some arctic and tropical mammals and birds. Biol. Bull., 1950, 99(2): 237-258.

Scholander, P. F.; Walters, V.; Hock, R. & Irving, L. Body insulation of some arctic and tropical mammals and birds. Biol. Bull., 1950, 99(2): 225-236.

Also try to see "Man in Cold Environment" by A.C. Burton & O.G. Edholm. Edward Arnold Ltd., London, 1955.

It is a classical monograph compiling intensive and extensive researches (including those by Scholander's) on thermal regulation caused by needs of military service in Arctic regions during WWII.

P.S.

Just some more remarks. Definitely, the heat balance studies in biology may be done only after J. Fourier's work on heat transfer published in 1822. But by 1884 the analytical tools developed for thermal transfer studies and engineering seems was already used to analyze heat balance of animals. In this year W. Tomson (Kelvin) reported in Edinburgh Royal Society "On the efficiency of clothing for maintaining temperature" where, among other, he discussed effectiveness of pelage as heat insulator in small endothermic animals and/or their appendages.

I agree with Yu F Ivlev's answer. I've cited the Scholander references for my work on marine mammal thermoregulation.  I'm also familiar with the book "Man in Cold Environment", but I never got my hands on a copy.

Hi William,

Just saw this post and had to respond. This is a fun topic. I had recently outlined some of the early history of work related to heat stress research that the military has kept up the thread on (Potter et al., 2017). This goes back to early work by Blagden (1775). However, I would also say there is a lot of really nice work outlined by Gagge and Gonzalez (1995) and more recent work by George Havenith (or most of anything that comes from him) (attached are a few).

Nice key references outlined by Yu also.

Fun topic!

-Adam