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A thermal model of a semiconductor structure is developed using a hierarchical function space, rather than physical space. The thermal model is derived using the proper orthogonal decomposition (POD) and does not require any assumptions about the physical geometry, dimensions, or heat flow paths, as is usually necessary for compact/lumped thermal models. The approach can be applied to complex geometries and provides detailed thermal information at a computational cost comparable to that of lumped thermal models. The POD thermal model is applied to steady thermal simulations of a 2-D silicon-on-insulator (SOI) device structure and validated at various power levels against detailed numerical simulation (DNS) data. It is shown that a POD thermal model using only four POD modes can duplicate the temperature solution derived from DNS, including the hot spot and temperature gradients along the device island. In addition, an unsteady POD model of the SOI device structure is constructed. A POD model incorporating ten modes yielded a virtually identical solution when compared to corresponding unsteady DNS results.