Pick-and-place (PnP) operations, featuring object grasping and trajectory planning, are fundamental in industrial robotics applications. Despite many advancements in the field, PnP is limited by workspace constraints, reducing flexibility. Pick-and-throw (PnT) is a promising alternative where the robot throws objects to target locations, leveraging extrinsic resources like gravity to improve efficiency and expand the workspace. However, PnT execution is complex, requiring precise coordination of high-speed movements and object dynamics. Solutions to the PnT problem are categorized into analytical and learning-based approaches. Analytical methods focus on system modeling and trajectory generation but are time-consuming and offer limited generalization. Learning-based solutions, in particular Model-Free Reinforcement Learning (MFRL), offer automation and adaptability but require extensive interaction time. This paper introduces a Model-Based Reinforcement Learning (MBRL) framework, MC-PILOT, which combines data-driven modeling with policy optimization for efficient and accurate PnT tasks. MC-PILOT accounts for model uncertainties and release errors, demonstrating superior performance in simulations and real-world tests with a Franka Emika Panda manipulator. The proposed approach generalizes rapidly to new targets, offering advantages over analytical and Model-Free methods.