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Jelly-roll type Nb-Al multifilamentary wires were rapidly heated to temperatures above 1800°C followed by quenching to room temperature, using experimental setups designed and built for this purpose. The ductile Nb-Al bcc solid solution retained by quenching is transformed by an 800°C/10h transformation heat treatment to superconducting Nb3Al of A15 structure. In the range of compositions investigated (23.5 to 35.0at% Al) the bcc phase was found to form by an endothermic reaction taking place during rapid heating. Optimal critical current densities (at 4.2K in magnetic fields exceeding 15T) were obtained for samples heated to maximum temperatures in a range of less than 200°C above the bcc formation reaction. At higher temperatures the bcc solid solution starts to melt, leading to inhomogeneity that degrades the critical current density. Samples quenched from fully liquid state exhibit large pores that can reduce the critical current density. X-ray diffraction and scanning electron microscopy on samples quenched from temperatures above and below the bcc formation temperature showed that at 23.5at% Al, an A15 structure Nb3Al formed in the earlier stages of the rapid heating massively transforms to bcc solid solution. A massive transformation is also found at 35.0at% Al, sigma-type Nb2Al converting to bcc solid solution. At 27.5at% Al, Nb3Al reacts eutectoidally with Nb2Al to form bcc solid solution. All these transformations were found reversible and heating rate independent. The bcc solid solution formation and the extended Al solubility reported could not be explained based on published Nb-Al equilibrium phase diagrams so it is concluded that none of them is correct and a revised phase diagram is proposed. All superconducting properties improved with increase in the initial heating rate associated with the transformation heat treatments. X-ray diffraction and transmission electron microscopy studies revealed that at low heating rates the spacing between certain planar faults is reduced which leads to poorer superconducting properties. At slow heating rates, prior to the transformation to A15, a B2 ordering of the bcc phase was found to proceed to a higher extent than for slow heating, which suggests a connection with the planar fault formation.