Early-stage and advanced breast cancer represent distinct disease processes. Thus, identifying the stage of tumor is a crucial procedure for optimizing treatment efficiency. Breast thermography has demonstrated significant advancements in non-invasive tumor detection. However, the accurate determination of tumor stage based on temperature distribution represents a challenging task, primarily due to the scarcity of thermal images labeled with the stage of tumor. This work proposes a transfer learning approach based on Deep Convolutional Neural Network (DCNN) with thermal images for predicting breast tumor stage. Various tumor stage scenarios including early and advanced tumors are embedded in a 3D breast model using the Finite Element Method (FEM) available on COMSOL Multiphysics software. This allows the generation of the thermal image dataset for training the DCNN model. A detailed investigation of the hyperparameters tuning process has been conducted to select the optimal predictive model. Thus, various evaluation metrics, including accuracy, sensitivity, and specificity, are computed using the confusion matrix. The results demonstrate the DCNN model's ability to accurately predict breast tumor stage from thermographic images, with an accuracy of 98.2%, a sensitivity of 98.8%, and a specificity of 97.7%. This study indicates the promising potential of thermographic images in enhancing deep learning algorithms for the non-invasive prediction of breast tumor stage.