Chiplet-based systems have gained significant attention in recent years due to their low cost and competitive performance. As the complexity and compactness of a chiplet-based system increase, careful consideration must be given to microbump assignments, interconnect delays, and thermal limitations during the floorplanning stage. This paper introduces RLPlanner, an efficient early-stage floorplanning tool for chiplet-based systems with a novel fast thermal evaluation method. RLPlanner employs advanced reinforcement learning to jointly minimize total wirelength and temperature. To alleviate the time-consuming thermal calculations, RLPlanner incorporates the developed fast thermal evaluation method to expedite the iterations and optimizations. Comprehensive experiments demonstrate that our proposed fast thermal evaluation method achieves a mean absolute error (MAE) of 0.25 K and delivers over 120x speed-up compared to the open-source thermal solver HotSpot. When integrated with our fast thermal evaluation method, RLPlanner achieves an average improvement of 20.28\% in minimizing the target objective (a combination of wirelength and temperature), within a similar running time, compared to the classic simulated annealing method with HotSpot.