“The most original work ever written in the physical sciences, with a core of abstraction comparable to the best of Galileo.”
Carnot's Reflections, in short, acted to launch the science of thermodynamics by introducing the now-famous conceptions and postulates of: Carnot cycle, Carnot engine, Carnot’s theorem, the definition of work, as in weight lifted through a height, among others. 
Carnot printed 600 copies of his Reflections. One copy was presented before the Academie. There was a long and appreciative review of it in one journal, a brief notice in another, and an encomium by Nicholas Clement who recommended it to students.  Other than this, it is said, for the next ten years the book went unnoticed.
Clapeyron's graphical analysis
In 1834, French physicist Émile Clapeyron revived Carnot's Reflections with his paper Memoir on the Motive Power of Heat, by presenting a graphical analysis, using Scottish engineer James Watt’s indicator diagrams, of the cycle described by Carnot. 
See main: search for Carnot’s ReflectionsIn 1839, at the Royal Belfast Academical Institution of Northern Ireland, where a young 15-year-old student William Thomson was in attendance, Scottish educator John Nichol, a professor of astronomy, took the chair of natural philosophy. That year, Nichol updated the curriculum, introducing the new mathematical works of Joseph Fourier. The mathematical treatment much impressed young Thomson, who became intrigued with Fourier's Théorie analytique de la chaleur and committed himself to study the "Continental" mathematics resisted by a British establishment still working in the shadow of English physicist Isaac Newton. In 1845, Thomson went on a famous search for Carnot’s Reflections.
This effort eventually resulted in the publication of his two famous articles: “On an Absolute Thermometric Scale Founded on Carnot’s Theory of the Motive Power of Heat” (1848) and “An Account of Carnot’s Theory of the Motive Power of Heat: with Numerical Results Deduced from Regnault’s Experiments on Steam” (1849), which eventually found their way into the hands of German physicist Rudolf Clausius, which resulted in launching of the science of thermodynamics. 
In German physicist Hermann Helmholtz’s 1847 memoir “On the Conservation of Force” gives mention of both Carnot and Clapeyron, which seems to be one of the first published revivals of Carnot’s work, Clapeyron aside.  Helmholtz cites their work on heat as illustrations of the sorts of causal explanations of which he approves, and notes they are premise upon the prohibition of perpetual motion. 
The first English translation was made by American mechanical engineer Robert Thurston in 1890 based on an 1878 French reprint.
1. Carnot, Sadi. (1824). “Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power.” Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55. (1890 English translation by Robert Thurston).
2. Clapeyron, Emile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX,  446, 566).
3. Shachtman, Tom. (1999). Absolute Zero and the Quest for Absolute Cold (pgs. 79-85). Mariner Books.
4. (a) Thomson, William. (1848). “On an Absolute Thermometric Scale Founded on Carnot’s Theory of the Motive Power of Heat” (pgs. 100-06), Cambridge Philosophical Society Proceedings for June 5; and Phil. Mag., Oct. 1848.
(b) Thomson, William. (1849). “An Account of Carnot’s Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault’s Experiments on Steam”, (127-203) Transactions of the Edinburgh Royal Society, xiv.; Annales de Chime, xxxv. 1852.
5. Helmholtz, Hermann. (1847). “On the Conservation of Force”, “Uber die Erhaltung der Kraft” (Carnot and Clapeyron, pgs. 7, 28), presented at the meeting of the Physical Society of Berlin on July 23; in: Selected Writings (Carnot, 4+ pgs). Russell Kahl, ed. Wesleyan University Press.
6. Mirowski, Philip. (1989). More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics (pg. 130). Cambridge University Press.
● Reflections on the Motive Power of Fire – Wikipedia.