The invention of novel methods is described for efficient and accurate thermal simulation of a structure that can be primarily constructed using building blocks. These structures may include, but not limited to, semiconductor chips, photovoltaic / solar panels, battery packs, etc. The methods are formulated in hierarchical function spaces, rather than the physical space and provide three-dimensional (3D) steady-state and transient temperature profiles of the structure, which are as detailed as full-scale numerical simulation, using substantially less computational degrees-of-freedom (DOF). The number of DOF required is comparable to that of lumped thermal models, yet no ad-hoc modeling assumptions related to geometry, dimensions, temperature profiles, or heat flow paths are required. The methods can be applied to evaluate temperature profiles at different levels of granularity. The methods can also be implemented in various computer-aided-design (CAD) or electronic-design-automation (EDA) tools for different technologies to perform electro-thermal simulations.