Provided significant future progress in artificial intelligence and computing, it may ultimately be possible to create multiple Artificial General Intelligences (AGIs), and possibly entire societies living within simulated environments. In that case, it should be possible to improve the problem solving capabilities of the system by increasing the speed of the simulation. If a minimal simulation with sufficient capabilities is created, it might manage to increase its own speed by accelerating progress in science and technology, in a way similar to the Technological Singularity. This may ultimately lead to large simulated civilizations unfolding at extreme temporal speedups, achieving what from the outside would look like a Temporal Singularity. Here we discuss the feasibility of the minimal simulation and the potential advantages, dangers, and connection to the Fermi paradox of the Temporal Singularity. The medium-term importance of the topic derives from the amount of computational power required to start the process, which could be available within the next decades, making the Temporal Singularity theoretically possible before the end of the century.