This paper presents a new transfer function approach for calculating both the average temperature and hot spot temperature of an induction machine with the consideration of temperature-dependent material properties and speed-dependent heat transfer coefficient. Green's functions are introduced and taken as the new transfer functions. Online thermal monitoring models for induction machines are obtained based on Green's function method. Using the presented method, the hot spot temperature and average temperature can be calculated accurately and rapidly. The proposed method is validated via finite-element method and experimental measurement.