Soft grippers in automation, particularly those with variable joint stiffness, offer promising possibilities for precise manipulation tasks. However, accurately predicting finger joint bending angles in this field poses significant challenges due to the soft and complex nature of the grippers, making modeling and angle prediction difficult. This paper presents the development of a predictive model for precisely controlling bending angles in multi-material printed soft grippers with variable stiffness, which are pivotal for delicate manipulation tasks in automation. In particular, we explore a cable-driven gripper design made of thermoplastic polyurethane and conductive polylactic acid materials, featuring integrated resistive joints for stiffness modulation through controlled Joule heating. A data-driven modeling approach, combining numerical modeling of the gripper and machine learning techniques, was employed for the development of the predictive model. We performed static structural simulations using ANSYS Workbench to measure bending angles under various conditions for developing datasets for model training. In this work, we evaluated several machine learning models such as linear regression, decision tree, and K-nearest neighbor regression models to predict the correlation between temperature, pull distance, and bending angle. The K-nearest neighbor regression model demonstrated the highest accuracy, with a mean absolute error of approximately 11%. These findings underline the importance of precise angle prediction models in enhancing the functionality and reliability of soft grippers, paving the way for their broader application in automation and robotics.