1. A computer-readable medium comprising computer-readable instructions for determining ampacity risks in a circuit, when executed by a computer causing the computer to: receive geometry data of the circuit; initialize boundary conditions; initialize circuit geometry assumptions; model the circuit geometry data as a three-dimensional solid; compute non-Fourier heat conduction through the three-dimensional solid model using conjugate gradient numerical analysis with an incomplete Cholesky preconditioner; and generate an output indicative of a location in the three-dimensional solid model where potential thermal damage may occur in response to a predetermined excitation wherein generating an output comprises generating an output in response to a transient aperiodic excitation.