Modern gas turbine blades and vanes are operated at temperatures above their material’s melting point. Active external and internal cooling are therefore necessary to reach acceptable lifetimes. One possible internal cooling method is called matrix cooling, where a matrix of intersecting cooling air channels is integrated into a blade or vane. To further increase the efficiency of gas turbines, the amount of cooling air must be reduced. Therefore it is necessary that heat transfer inside a cooling matrix is well understood. In the first part of the thesis, a methodology for estimating heat transfer in the flow of matrix cooling channels was established using Computational Fluid Dynamics. Two four-equation RANS turbulence models based on the k-ε turbulence model showed a good correlation with experimental results, while the k-ω SST model underpredicted the heat transfer significantly. For all turbulence models, the heat transfer showed high sensitivity towards changes in the numerical setup. For the k-ω SST turbulence model, the mesh requirements were deemed too computationally expensive and it was excluded from further investigations. As the second part of the thesis, a parameter study was conducted investigating the influence of several geometric parameters on the heat transfer in a cooling matrix. The matrix was simplified as a channel flow interacting with multiple crossing flows. The highest enhancement in heat transfer was seen with changes in taper ratio, aspect ratio and matrix angle. Compared to smooth pipe flow, an increase in heat transfer of up to 60% was observed. Rounded edges of the cooling channels showed a significant influence on the heat transfer as well. In contrast, no influence of the wall thickness on the heat transfer was observed. While no direct validation is possible, the base case and the parameter sweeps show a good correlation with similar cases found in the literature.