The ability to improve protein thermostability via protein engineering is of great scientific interest and also has significant practical value. In this report we present PROTS-RF, a robust model based on the Random Forest algorithm capable of predicting thermostability changes induced by not only single-, but also double- or multiple-point mutations. The model is built using 41 features including evolutionary information, secondary structure, solvent accessibility and a set of fragment-based features. It achieves accuracies of 0.799,0.782, 0.787, and areas under receiver operating characteristic (ROC) curves of 0.873, 0.868 and 0.862 for single-, double- and multiple- point mutation datasets, respectively. Contrary to previous suggestions, our results clearly demonstrate that a robust predictive model trained for predicting single point mutation induced thermostability changes can be capable of predicting double and multiple point mutations. It also shows high levels of robustness in the tests using hypothetical reverse mutations. We demonstrate that testing datasets created based on physical principles can be highly useful for testing the robustness of predictive models.