Cutting of metal is a complex physical process. Evolving temperature distributions in chip, tool and work piece, thereby, have major significance for the process and the related outcomes. Present analytical models are not capable to predict temperature fields to a sufficient degree. This lack of model validity is caused, amongst other reasons, by the limited mathematical approaches. Particularly, mainly only real-valued functions were taken into account for most analytical models. The present thesis deals with the development of methodologies for thermal modeling based on a class of complex functions termed potential functions. In the contribution, the basics of these functions and the relevant state of art is provided. An initial simple approach for derivation of a complex model is based on the elementary solutions of potential theory. While this approach can be regarded as a feasibility study, another more systematic methodology based on a discretization approach is presented as the core development of this thesis. The systematic method explicitly considers boundary conditions and geometry, which are characteristic for the metal cutting process. This systematic is based on the so-called Panel Method. An introduction to this theory, the application for the metal cutting process and detailed discussion about the model outcomes are provided. To validate both novel approaches, validation experiments were conducted on a fundamental test rig and a broaching machine. For the validation, a measurement method combining infrared camera and two-color pyrometer was developed. The objective of this method is to decrease measurement uncertainty opposite to the single use of each measurement device. Finally in the thesis an assessment of the developed methodologies compared to conventional analytical modeling approaches and discretization methods is provided.