It's not smoke visible on the underside of the aircraft, it's steam, this article has some interesting information about the aircraft's cooling system:
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Power and reliability would come from Shanholtzer’s hot-rodded V-12 Merlin. In a big move, the drag reduction part of the equation came from removing the Mustang’s iconic belly scoop. The function of the radiator and oil cooler would be combined in a heat exchanger, and that would be placed in a tank of water/methanol. As hot coolant and engine oil flowed through the exchanger, heat would transfer to the water/meth where it would boil and vent overboard. The whole idea was to have zero cooling drag on the airplane. In fact, the only air coming into the airplane is fed to the engine. Since the late 1940s, The Galloping Ghost is only the fourth racing P-51 to undergo this surgery. If done right, it has some big benefits to offer.