As electrical and electronics engineers have striven to create more energy-dense and efficient designs, thermal non-idealities have risen to the forefront of such design endeavors as impediments to miniaturizing and densifying electrical products. In order to overcome these thermal design barriers, engineers require detailed prediction of their circuits' thermal characteristics. Modern electrical engineers must often understand the thermal dynamics of their systems equally as well as the electrical characteristics. In this thesis, an overview of electrical design areas affected by thermal concerns is given, and a literature review of thermal modeling techniques commonly utilized in electrical designs is provided. Furthermore, the thermal modeling of atomic clock mechanical structures is identified as the primary focus of this thesis, and the well-known Cauer electro-thermal circuit framework for thermal modeling is identified as an optimal modeling solution for atomic clock geometries. Subsequently, a full description of the Cauer model and its associated conductive, convective, and radiant physics is given with specific emphasis on atomic clock thermal modeling. Additionally, experimental and numerical techniques utilized in the extraction of Cauer network parameters are discussed, and background on the practical implementation and physical behavior of thermal sensors is given. Last, experimental validation of the Cauer model and its applicability to atomic clock geometries is shown through the application of the techniques and theories discussed in this thesis.