Copper as a material with a high electrical and thermal conductivity awakes large interest for many applications in industry, e.g. thermal management of electronic components. Powderbased manufacturing techniques (e.g. Selective Laser Melting, Binder Jetting, Fused Filament Fabrication and Metal Injection Molding) enable the complex shaping of metals. Especially the methods without melting processes like Binder Jetting, Fused Filament Fabrication and Metal Injection Molding have a great potential for complex Cu structures. These techniques built up a powder-based green body and require a subsequent sintering step to reach a high density with maximum properties. This work reports the development of the heat conductivity during pressure-less sintering of Cu powder green bodies. The experimental results are compared to analytical models and a numerical simulation and show the limits of the reachable heat conductivity depending on the remaining porosity and the impurity concentration.