Modern digital manufacturing processes, such as additive manufacturing, are cyber-physical in nature and utilize complex, process-specific simulations for both design and manufacturing. Although computational simulations can be used to optimize these complex processes, they can take hours or days — an unreasonable cost for engineering teams leveraging iterative design processes. Hence, more rapid computational methods are necessary in areas where computation time presents a limiting factor. When existing data from historical examples is plentiful and reliable, supervised machine learning can be used to create surrogate models that can be evaluated orders of magnitude more rapidly than comparable finite element approaches. However, for applications that necessitate computationally-intensive simulations, even generating the training data necessary to train a supervised machine learning model can pose a significant barrier. Unsupervised methods, such as physics-informed neural networks, offer a shortcut in cases where training data is scarce or prohibitive. These novel neural networks are trained without the use of potentially expensive labels. Instead, physical principles are encoded directly into the loss function. This method substantially reduces the time required to develop a training dataset, while still achieving the evaluation speed that is typical of supervised machine learning surrogate models. We propose a new method for stochastically training and testing a convolutional physics-informed neural network using the transient 3D heat equation- to model temperature throughout a solid object over time. We demonstrate this approach by applying it to a transient thermal analysis model of the powder bed fusion manufacturing process.