In this paper a three-dimensional conjugate calculation has been performed for a passenger car turbo charger. The scope of this work is to investigate the heat fluxes in the radial compressor which can be strongly influenced by the hot turbine. As a result of this, the compressor efficiency may deteriorate. Consequently, the heat fluxes have to be taken into account for the determination of the efficiency. To overcome this problem a complex three-dimensional model has been developed. It contains the compressor, the oil cooled center housing, and the turbine. 12 operating points have been numerically simulated composed of three different turbine inlet temperatures and four different mass flows. The boundary conditions for the flow and for the outer casing were derived from experimental test data (part II of the paper). Resulting from these conjugate calculations various one-dimensional calculation specifications have been developed. They describe the heat transfer phenomena inside the compressor with the help of a Nusselt number which is a function of an artificial Reynolds number and the turbine inlet temperature.