This paper proposes a new method for an optimized mapping of temporal variables, describing a temporal stream data, into the recently proposed NeuCube spiking neural network (SNN) architecture. This optimized mapping extends the use of the NeuCube, which was initially designed for spatiotemporal brain data, to work on arbitrary stream data and to achieve a better accuracy of temporal pattern recognition, a better and earlier event prediction, and a better understanding of complex temporal stream data through visualization of the NeuCube connectivity. The effect of the new mapping is demonstrated on three benchmark problems. The first one is the early prediction of patient sleep stage event from temporal physiological data. The second one is the pattern recognition of dynamic temporal patterns of traffic in the Bay Area of California and the last one is the Challenge 2012 contest data set. In all the cases, the use of the proposed mapping leads to an improved accuracy of pattern recognition and event prediction and a better understanding of the data when compared with traditional machine learning techniques or SNN reservoirs with an arbitrary mapping of the variables.