We propose a simulated annealing approach for the examination timetabling problem, as formulated in the 2nd International Timetabling Competition. We apply a single-stage procedure in which infeasible solutions are included in the search space and dealt with using suitable penalties. Upon our approach, we perform a statistically-principled experimental analysis, in order to understand the effect of parameter selection on the performance of our algorithm, and to devise a feature-based parameter tuning strategy, which can achieve better generalization on unseen instances with respect to a one-fits-all parameter setting. The outcome of this work is that this rather straightforward search method, if properly tuned, is able to compete with all state-of-the-art specialized solvers on the available instances. As a byproduct of this analysis, we propose and publish a new, larger set of (artificial) instances that could be used for tuning and also as a ground for future comparisons.