He may have been a pupil of Josiah R. Brady, the architect, for among the drawings in the New York Historical Society is one of the Merchants' Exchange, credited in the handwriting of a contemporary to J. R. Brady and M. E. Thompson.
He was commissioned in 1822-23 to design the second Bank of the United States on Wall Street, later the United States Assay Office (1854 - 1915), its lovely façade now serving as the south front of the American wing of the Metropolitan Museum of Art. In 1824 he was called on for a design for the Merchants' Exchange, completed in July 1827 and burned in the great fire of 1835. In beauty and richness the building had no peers in the city. It was dignified, simple, and commodious, and the Exchange Room, 85 by 55 feet, with rounded ends and a screen of columns, was well proportioned and impressive. It is shown in one of the Pendleton lithographs of New York.
By 1827 Thompson had formed a partnership with Ithiel Town. Their office at 32 Merchants' Exchange soon became an artistic center, and was opened as an "Architectural Room" to those who wished to consult Town's magnificent library of architectural books and engravings. The effect on Thompson was to convert him at once to the Greek Revival. In their combined work--especially in the Church of the Ascension (1828) on Canal Street, and in the brick tower and spire of St. Mark's in the Bowery (still standing, 1935) – Town may have had a great part, though Minard Lafever in The Young Builder's General Instructor (Newark, 1829) gives Thompson the credit for the Church of the Ascension, and a Mr. Morris in the New York Mirror, March 1, 1828, in praising the St. Mark's steeple for its beauty and its omission of such "pretty things" as the common brazen weathercock, mentions only Thompson's name.
In 1826 Thompson was one of the thirty founders of the National Academy of Design. Both he and Town exhibited there regularly until about 1833. Their partnership seems to have ended in 1828, for in 1829 Thompson exhibited several designs alone. He was the designer of the Columbia Grammar School (begun 1829), the façades of the houses on the Murray Street lots of Columbia University, and the noted house of Robert Ray, 17 Broadway, burned in the great fire of 1845. In 1839 he received the second premium in the competition for the Ohio capitol at Columbus. He made several plans for the enlargement of the City Hall.
From May 1847 to January 1850 he served as street commissioner of New York City. He lived on East Eleventh Street, 1844-53, and on West Twelfth, 1853-64. After the death of his wife, he seems to have left New York and retired to Glen Cove, L. I, where he died.
As a designer Thompson ranks high. The second Bank of the United States is gracious, restrained, delicate, rather in the English tradition, as was the Ray house. The Merchants' Exchange was more original, more daring, more powerful; the recessed portico was a new note, its cupola was unusually effective, and its large Exchange Room both delicate and monumental. The St. Mark's spire is markedly original in conception in its avoidance of the orders, the Columbia Grammar School was well massed, and the plans for the City Hall extensions reveal great planning ability. The Columbia houses are simple and straightforward, and give stylistic support to the assumption that Thompson was probably the architect of many of those dignified houses built in the northern part of Greenwich Village in the forties and fifties.
Besides being one of the founders of the National Academy of Design he was a member of the General Society of Mechanics and Tradesmen from 1822 on.
He married Mary (who was born in New York City and died there, February 9, 1864, at the age of seventy-five).