Generating energy from nuclear fusion in a tokamak may highly benefit from precise control of both kinetic and magnetic spatially-varying properties of the plasma (hot ionized gas where the fusion reactions take place). The spatial dependence of a plasma property, from the core to the edge of the plasma, is referred to as profile. Many control algorithms being developed require accurate, real-time knowledge of the plasma space-dependent state. However, many of the diagnostics used to measure the plasma state provide data that can be noisy or require significant post-processing. Within this context, an observer has been developed using an extended Kalman filtering approach for the electron temperature profile. The model employed by the observer uses a combination of analytical components and trained neural networks to generate as accurate of a prediction as possible while working within real-time calculation constraints. Such neural networks provide high accuracies, fast calculation times, and wide applicability. In addition, with only two diagnostic measurements at different spatial locations, the observer is able to estimate the entire electron temperature profile. Simulation results show that the observer can correctly estimate this profile despite significant discrepancies in the initial electron temperature profile and relatively high levels of noise. After its implementation in the plasma control system of the DIII-D tokamak, this observer may be able to provide valuable information on the electron temperature to a variety of present and future controllers.