The benefits of plants for the production of biopharmaceutical proteins include the ease of scale-up and the low pathogen burden, but the purification of target proteins is often affected by low expression levels and the abundance of host cell proteins in leaf extracts. These factors can significantly diminish the competitiveness of plant-based expression systems. We therefore compared three different heat precipitation steps that remove most host cell proteins while leaving a heat-stable candidate malaria vaccine protein in solution. A design-of-experiments approach was used to test each method and analyze the resulting data, allowing us to model and optimize the corresponding process. The heat treatment of leaves was superior to both methods for the heat treatment of extracts in terms of process-scale implementation, energy consumption and speed. We discuss additional benefits and drawbacks of these methods compared to current strategies for the purification of biopharmaceutical proteins produced in plants.