Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical to preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions and online control in iterative design scenarios. Conversely, machine learning models rely heavily on high-quality datasets, which can be costly and challenging to obtain within the metal AM domain. Our work addresses this by introducing a physics-informed neural network framework specifically designed for temperature field prediction in metal AM. This framework incorporates a physics-informed input, physics-informed loss function, and a Convolutional Long Short-Term Memory (ConvLSTM) architecture. Utilizing real-time temperature data from the process, our model predicts 2D temperature fields for future timestamps across diverse geometries, deposition patterns, and process parameters. We validate the proposed framework in two scenarios: full-field temperature prediction for a thin wall and 2D temperature field prediction for cylinder and cubic parts, demonstrating errors below 3% and 1%, respectively. Our proposed framework exhibits the flexibility to be applied across diverse scenarios with varying process parameters, geometries, and deposition patterns.