The objective of this research is to study an effective thermal data stream prediction method for additive manufacturing (AM) processes using thermal image streams in a layer-wise manner. Reliable physics-based models have been developed to delineate the underlying thermomechanical dynamics of AM processes. However, the computational cost is extremely high. We proposed a tensor-based surrogate modeling methodology to predict the layer-wise relationship in thermal data stream of the AM parts, which is time efficient compared to available physics-based prediction models. We constructed a network tensor structure for freeform shapes based on thermal image streams obtained in metal-based AM processes. Then, we simplified the network tensor structure by concatenating images to reach a layer-wise structure. Subsequent layers were predicted based on the antecedent layer using the tensor regression model. A generalized multilinear structure, called the higher order partial least squares (HOPLS), was used to estimate the tensor regression model parameters. Through the proposed method, high-dimensional thermal histories of AM components were predicted accurately in a computationally efficient manner. Prediction performance indices (i.e., and root-mean-square errors of prediction (RMSEP) = 31.212 °C) demonstrated a significantly more efficient layer-wise prediction of thermal data stream—a larger Q2 (0 ≤ Q2 ≤ 1) and a smaller RMSEP indicated a better prediction performance. The proposed thermal data stream prediction was validated on simulated thermal images from finite element (FE) simulations.