The pattern placement accuracy of a stencil mask is affected by thermomechanical distortion induced during ion beam exposure. Any temperature gradient across the mask membrane could result in thermal distortions which contribute to the stringent error budget. Therefore, a concept has been proposed to control the temperature across the mask membrane by using radiation heat transfer between exposure station components. This work extends previous efforts by including the effects of the backside radiation loss of the exposure area, the aperture, etc. Here the exposure station which has been proposed by IMS-Ion Microfabrication Systems is investigated and simulated with finite element models. Parametric studies have been performed in order to optimize design variables such as material properties, and the temperature settings of the cooled lens electrodes and aperture.