  Modern experiments aiming at tests of fundamental physics, like measuring
gravitational waves or testing Lorentz Invariance with unprecedented accuracy,
require thermal environments that are highly stable over long times. To achieve
such a stability, the experiment including typically an optical resonator is
nested in a thermal enclosure, which passively attenuates external temperature
fluctuations to acceptable levels. These thermal shields are usually designed
using tedious numerical simulations or with simple analytical models. In this
paper, we propose an accurate analytical method to estimate the performance of
passive thermal shields in the frequency domain, which allows for fast
evaluation and optimization. The model analysis has also unveil interesting
properties of the shields, such as dips in the transfer function for some
frequencies under certain combinations of materials and geometries. We validate
the results by comparing them to numerical simulations performed with
commercial software based on finite element methods.
