Educational games are being increasingly used to support self-paced learning. However, educators and system designers often face challenges in monitoring student affect and cognitive load. Existing assessments in game-based learning environments (GBLEs) tend to focus more on outcomes rather than processes, potentially overlooking key aspects of the learning journey that include learner affect and cognitive load. To address this issue, we collected data and trained a model to track learner cognitive load while they used an online literacy game for English. We collected affect-related physiological data and pupil data during gameplay to enable the development of models that identify these latent characteristics of learner processes. Our model indicates the feasibility of using these data to track cognitive load in GBLEs. Our multimodal model distinguished different levels of cognitive load, achieving the highest Kappa (.417) and accuracy (70%). Our model reveals the importance of including affect-related features (i.e., EDA and heart rate) when predicting cognitive load and extends recent findings suggesting the benefit of using multiple channels when modeling latent aspects of learner processes. Findings also suggest that cognitive load tracking could now be used to facilitate the creation of personalized learning experiences.