Meta-modeling helps to reduce the computational cost of large-scale stochastic simulations. It, however, brings froth additional uncertainty in the prediction. In this work, we illustrate the use of the Response Surface Method (RSM) and Gaussian Process (GP) regression to approximate the cold-side temperature of a fire barrier in a stochastic compartment fire scenario. The deterministic model is a 1D Finite Element Method (FEM) solving heat-diffusion. We also illustrate a method for the quantification and compensation of the meta-modeling uncertainty. Additionally, we present a simple technique to create a RSM model with an arbitrary order polynomial function. The results show that both RSM and GP model can produce accurate stochastic simulations despite only few deterministic data points. The simple polynomial-based RSM approximation, however, fails when the heat-transfer is affected by exothermic reactions. This is in contrast with GP, where the combination of various kernel functions makes the prediction flexible enough even for the highly non-linear problem. The meta-modeling uncertainty can be quantified during the testing of meta-models and later be used to improve the accuracy of stochastic predictions.