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Climate change projections are commonly based on multi-model ensembles of climate simulations. In this paper we consider the choice of bias models in Bayesian multimodel predictions. Buser et al. (Clim Res 44(2-3):227-241, 2010a) introduced a hybrid bias model which combines commonly used constant bias and constant relation bias assumptions. The hybrid model includes a weighting parameter which balances these bias models. In this study, we use a cross-validation approach to study which bias model or bias parameter leads to, in a specific sense, optimal climate change projections. The analysis is carried out for summer and winter season means of 2 m-temperatures spatially averaged over the IPCC SREX regions, using 19 model runs from the CMIP5 data set. The cross-validation approach is applied to calculate optimal bias parameters (in the specific sense) for projecting the temperature change from the control period (1961-2005) to the scenario period (2046-2090). The results are compared to the results of the Buser et al. (Clim Res 44(2-3):227-241, 2010a) method which includes the bias parameter as one of the unknown parameters to be estimated from the data. [ABSTRACT FROM AUTHOR]