Designing and clearing day-ahead electricity market auctions have recently received significant attention from academia and practice alike. Given the size and the complexity of day-ahead market auctions, clearing them within the time limits imposed by the market is a major practical concern. In this paper, we model all the practical details of the Turkish day-ahead electricity market and provide a new multi-level iterative heuristic to clear the market. We compare our results with a commercial solver using data provided by Energy Exchange Istanbul. Our heuristic achieves an average optimality gap less than 0.09%, with an average solution time of just 14 s; whereas the commercial solver takes, on average, 18 min (and in some cases up to three hours) to find the optimal solution. We also demonstrate that using our heuristic solution to warm-start the commercial solver further reduces the solution time by 25%, on average. Overall, our heuristic proves to be very efficient in clearing the Turkish day-ahead market. We also test the performance of our algorithm as the problem size grows.