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A method based on the Karhunen-Loeve (KL) transform is proposed for the reduction of large-scale, nonlinear ordinary differential equations such as those arising from the finite difference modeling of biological heat transfer. The method of snapshots is used to expedite computation of the required quantities in the KL procedure. Guidelines are presented and validated for snapshot selection and resultant basis series truncation, emphasizing the special physical features of the electromagnetic phased-array heat transfer physics. Applications to fast temperature prediction are presented.