Theory of heat
In the history of science, the theory of heat or mechanical theory of heat was a theory, introduced in 1798 by Sir Benjamin Thompson, better known as Count Rumford and developed more thoroughly in 1824 by the French physicist Sadi Carnot, that heat and mechanical work are equivalent.  It is related to the mechanical equivalent of heat. Over the next century, with the introduction of the second law of thermodynamics in 1850 by Rudolf Clausius, this theory evolved into the science of thermodynamics. In 1851, in his "On the Dynamical Theory of Heat", William Thomson outlined the view, as based on recent experiments by those such as James Joule, that “heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect.” 
In the years to follow, the phrase the "dynamical theory of heat" slowly evolved into the new science of thermodynamics. In 1876, for instance, American civil engineer Richard Sears McCulloh, in his Treatise on the Mechanical Theory of Heat, stated that: “the mechanical theory of heat, sometimes called thermo-dynamics, is that branch of science which treats of the phenomena of heat as effects of motion and position.”
This term was used in 19th centuries to describe a number of laws, relations, and experimental phenomenon in relation to heat; those such as thermometry, calorimetry, combustion, specific heat, and discussions as to the quantity of heat released or absorbed during the expansion or compression of a gas, etc. One of the most famous publications, in this direction, was the Scottish physicist James Clerk Maxwell’s 1871 book Theory of Heat, which introduced the world to Maxwell's demon, among others. Another famous paper, preceding this one, is the 1850 article On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat by the German physicist and mathematician Rudolf Clausius in which the concept of entropy began to take from.
The term “theory of heat”, being associated with either vibratory motion or energy, was generally used in contrast to the caloric theory, which views heat as a fluid or a weightless gas able to move in and out of pores in solids and found between atoms. However, both these viewangles are actually compatible under the principle of energy conservation and corresponding first law of thermodynamics.
From modern perspective, the formal equivalence of heat and mechanical vibrations (or motions) does not mean they are physically identical. The fundamental difference of these two concepts shows particularly clearly in spectroscopy. While sharp spectral lines are usually associated with mechanical vibrations, the heat shows only a "random" spectrum with some distribution function (white noise, etc.)
 See also
- History of thermodynamics
- Larmor formula
- Timeline of thermodynamics, statistical mechanics, and random processes
- Thompson, Benjamin. Philosophical Transactions of the Royal Society of London, 1798, Part I, page 86
- Clausius, Rudolf. (1879). Mechanical Theory of Heat, 2nd Edition. London: Macmillan & Co.
- Thomson, William. (1951). “On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam.” Excerpts. [§§1-14 & §§99-100], Transactions of the Royal Society of Edinburgh, March, 1851; and Philosophical Magazine IV. 1852, [from Mathematical and Physical Papers, vol. i, art. XLVIII, pp. 174]
- Maxwell, James, C. (1871). Theory of Heat. Dover Publications, Inc. ISBN 0-486-41735-2.
- Clausius, Ruldolf (1850). On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat. Poggendorff's Annalen der Physick, LXXIX (Dover Reprint). ISBN 0-486-59065-8.
- Fourier and the Theory of Heat – Massachusetts Institute of Technology
- Mechanical Theory of Heat - Rochester Institute of Technology
- Heat – Eric Weisstein’s World of Physics (has good "theory of heat" book reference list)
-  The collected works of Count Rumford, who amongst others, began to seriously question the caloric or substance theory of heat, proposing in its place the modern theory of heat.