James Beaumont Neilson, previously foreman at Glasgow gas works, invented the system of preheating the blast for a furnace.  He found that by increasing the temperature of the incoming air to 300 degrees Fahrenheit, he could reduce the fuel consumption from 8.06 tons of coal to 5.16 tons of coal per ton of produced iron with further reductions at even higher temperatures.  He, with partners including Charles Macintosh, patented this in 1828.  Initially the heating vessel was made of wrought iron plates, but these oxidized, and he substituted a cast iron vessel.
On the basis of a January 1828 patent, Thomas Botfield has a historical claim as the inventor of the hot blast method. Neilson is credited as inventor of hot blast, because he won patent litigation. Neilson and his partners engaged in substantial litigation to enforce the patent against infringers. The spread of this technology across Britain was relatively slow.  By 1840, 58 ironmasters had taken out licenses, yielding a royalty income of £30,000 per year. By the time the patent expired there were 80 licenses. In 1843, just after it expired, 42 of the 80 furnaces in south Staffordshire were using hot blast, and uptake in south Wales was even slower.
Other advantages of hot blast were that raw coal could be used instead of coke. In Scotland, the relatively poor "black band" ironstone could be profitably smelted.  It also increased the daily output of furnaces. In the case of Calder ironworks from 5.6 tons per day in 1828 to 8.2 in 1833, which made Scotland the lowest cost steel producing region in Britain in the 1830s.
Early hot blast stoves were troublesome, as thermal expansion and contraction could cause breakage of pipes.  This was somewhat remedied by supporting the pipes on rollers.  It was also necessary to devise new methods of connecting the blast pipes to the tuyeres, as leather could no longer be used.
Ultimately this principle was applied even more efficiently in regenerative heat exchangers, such as the Cowper stove (which preheat incoming blast air with waste heat from flue gas; these are used in modern blast furnaces), and in the open hearth furnace (for making steel) by the Siemens-Martin process.
Independently, George Crane and David Thomas, of the Yniscedwyn Works in Wales, conceived of the same idea, and Crane filed for a British patent in 1836. They began producing iron by the new process on February 5, 1837. Crane subsequently bought Gessenhainer's patent and patented additions to it, controlling the use of the process in both Britain and the US. While Crane remained in Wales, Thomas moved to the US on behalf of the Lehigh Coal & Navigation Company and founded the Lehigh Crane Iron Company to utilize the process.