Various burn-in procedures have been greatly used to screen weak items and reduce warranty costs. This paper proposes a new burn-in model for heterogeneous items with non-renewing two-dimensional warranty. All failures within burn-in and warranty are assumed to be repaired through the minimal repair. Then we screen the items according to the failure information of the items during burn-in. We establish a cost-based model to optimize the mean total cost of each item put into the market. We demonstrate that the optimal burn-in time or usage rate should reach its upper bound under some conditions. In practice, the reliability and mean total cost of an item may be random due to the uncertainty of parameters in the model. Therefore, we also propose a Bayesian method to calculate the mean total cost and optimal burn-in policy of an item, which fully considers the uncertainty of parameters in the model. An example is also given to demonstrate the proposed burn-in model and Bayesian method.