The P-51H was the direct result of the experimental lightweight Mustangs that North American began working on in early-mid 1943, which included the XP-51F, XP-51G, and XP-51J. The lightweight Mustangs came about after the USAAF wanted to know why their fighter planes were heavier than British fighter planes, and why, for instance, that a comparable Mark of Spitfire could climb to a set altitude in 2/3 the time it would take the Mustang, or why the Fw 190 had twice the roll rate of the Mustang. Thus, they wanted to know if the design could be improved to match or better the performance of those other nation's fighters. Edgar Schmued of North American Aviation was sent to Britain in February of 1943 for two months to meet with British designers to compare design and production techniques (this included visits to de Havilland and to Rolls-Royce, where he was shown the latest Merlin engine (2200 hp, 120-in MP), which he wanted to get installed into a new Mustang design).
Here is some interesting information that Schmued wrote about, after studying the 'whys' that the American fighters were built heavier than their British counterparts. "First, the high angle of attack-load factor was 12 in America, but only 11 in England. Second, there was a side-load factor on the engine mount in America of 2G, which the British didn't have at all. Then the landing gear load factors that we used were 6G's, but were only 4G's in England. We used all of these factors to help whittle out a good deal of weight in a new design."
With the XP-51F, for example, which was essentially an entirely new design, they were able to shave 600 lbs. They did new things like making part of the engine cowl at the engine mount a structural member of the engine mount, and on the fuselage, aft of the firewall, they used .042 skins rather than .065 skins. Just about everything throughout the aircraft, including the main and tail gear, were redesigned to save on weight. The lightweight Mustangs are also sometimes referred to as the 'plastic Mustangs', as there was much more use of phenolic resin (an early plastic), such as using it to back some of the parts made of thinner aluminum. Some general characteristics of the lightweights included a longer canopy, which helped smooth out the airflow much better than the D-canopy, and the radiator scoop was stretched out for the same reason. Smaller main wheels and redesigned landing gear allowed for the leading edge of the wings to no longer be angled at the leading edge root.
The P-51H started coming off the assembly line at Inglewood in mid-1945, alongside some of the last D-models Inglewood would produce. The P-51H would never see combat in WWII or in the Korean War, but they were active throughout the late 40's and early 50's with the Air National Guard. The P-51H utilized the Merlin V-1650-9 engine, which produced 2,218 hp with water injection (this same engine can be and has been fitted to D-models, with some minor modifications as outlined in a tech order). Currently there are two P-51H's that are airworthy and flown, and I know of at least one other, maybe two, which be made airworthy.
It should be added, that while the XP-51F, G, and J never reached factory production, it wasn't the fault of North American, but rather a change in planning (a change of mind) by the USAAF. All of the experimental lightweight Mustangs achieved or exceeded their design goals. NAA's chief test pilot, Bob Chilton, for example, referred to the XP-51F as his favorite of all of the Mustangs built.