The third medium contact approach has been successfully employed in structural applications and extended to various optimization problems. This discretization technique replaces classical contact formulations and algorithms by introducing a compliant interfacial layer - referred to as the third medium - between the contacting bodies. Unlike traditional contact methods, this formulation naturally accommodates finite deformations at the interface. As bodies approach each other, the third medium undergoes compression and effectively acts as a deformable barrier, preventing interpenetration and transmitting contact forces in a smooth and numerically stable manner. The approach can be applied to coupled problems as well, with focus on thermo-mechanical analysis.Then heat conduction must be incorporated into the model, which typically requires specialized interface laws when using classical contact formulations. These laws aim to capture the complex thermal behavior at the contact interface, including discontinuities and varying conductance. In contrast, the third medium approach offers the advantage to account for the interface behavior without the need for additional interface conditions. This allows gradual heat transfer through the surrounding gas when the bodies are approaching each other. Once in contact the localized heat conduction is recovered. As a result, the third medium naturally captures both non-contact and contact-phase thermal conduction within a unified framework. In this talk, we discuss different approaches that can be applied when modeling third media contact. The discretization is carried out using linear and quadratic finite and virtual elements which are then applied to mechanical and thermo-mechanical contact problems in two- and three-dimensions.