This paper is part of a two-part publication that aims to design, simulate and test an internally air cooled radial turbine. To achieve this, the additive manufacturing process, Selective Laser Melting (SLM), was utilized to allow internal cooling passages within the blades and hub. This is, to the authors' knowledge, the first publication in the open literature to demonstrate an SLM manufactured, cooled concept applied to a small radial turbine. In this paper, the internally cooled radial turbine was investigated using a Conjugate Heat Transfer (CHT) numerical simulation. Topology Optimisation was also implemented to understand the areas of the wheel that could be used safely for cooling. In addition, the aerodynamic loss and efficiency of the design was compared to a baseline noncooled wheel. The experimental work is detailed in Part 2 of this two-part publication. Given that the aim was to test the rotor under representative operating conditions, the material properties were provided by the SLM technology collaborator. The boundary conditions for the numerical simulation were derived from the experimental testing where the inlet temperature was set to 1023 K. A polyhedral unstructured mesh made the meshing of internal coolant plenums including the detailed supporting structures possible. The simulation demonstrated that the highest temperature at the blade leading edge was 117 K lower than the uncooled turbine. The coolant mass flow required by turbine was 2.5% of the mainstream flow to achieve this temperature drop. The inertia of the turbine was also reduced by 20% due to the removal of mass required for the internal coolant plenums. The fluid fields in both the coolant channels and downstream of the cooled rotor were analyzed to determine the aerodynamic influence on the temperature distribution. Furthermore, the solid stress distribution inside the rotor was analyzed using Finite Element Analysis (FEA) coupled with the CFD results.