The electron cyclotron emission (ECE) diagnostic provides routinely electron temperature (Te) measurements. At ASDEX Upgrade an electron cyclotron forward model, solving the radiation transport equation for given Te and electron density profile, is used in the framework of integrated data analysis. With this method Te profiles can be obtained from ECE measurements even for plasmas with low optical depth. However, due to the assumption of straight lines of sight and an absorption coefficient in the quasi-perpendicular approximation this forward model is not suitable for the interpretation of measurements by ECE diagnostics with an oblique line of sight. Since radiation transport modelling is required for the interpretation of oblique ECE diagnostics we present in this paper an extended forward model that supports oblique lines of sight. To account for the refraction of the line of sight, ray tracing in the cold plasma approximation was added to the model. Furthermore, an absorption coefficient valid for arbitrary propagation was implemented. Using the revised model it is shown that for the oblique ECE Imaging diagnostic at ASDEX Upgrade there can be a significant difference between the cold resonance position and the point from which most of the observed radiation originates.