Fast radiative transfer codes have been developed for simulating the outgoing radiance (and corresponding brightness temperature) to be measured by the Infrared Imaging Radiometer (IIR) of the space Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission. Two simple codes (FASRAD and FASAA), for which scattering is neglected, as well as an accurate code (FASDOM), accounting for scattering and absorption with the Discrete Ordinate Method (DOM), are presented. Their accuracy has been estimated with a reference code including a line-by-line model and the DOM. Simulations have shown that the accuracy is generally better than 0.3 K on the brightness temperature for clear or cloudy atmospheres. This accuracy agrees with the expected one of future IIR measurements. In addition, the impact of scattering on the brightness temperature has been evaluated for semi-transparent liquid clouds in the IIR spectral range. Especially, simulations have shown that cloud microphysics retrieval might be possible with the Brightness Temperature Difference (BTD) between two IIR bands, using the couple of wavelengths (8.7-12 mm) or (10.6-12 mm). However, scattering strongly influences the radiation for shorter wavelengths. The error on the BTD with (8.7-12 mm) can reach 4 K when scattering is neglected, leading to large uncertainties in the retrieval of droplet effective radius.