Rapid and accurate wildfire detection is crucial for emergency response and environmental management. In airborne and spaceborne missions, real-time algorithms must distinguish between no fire, active fire, and post-fire conditions, and estimate fire intensity. Multispectral and hyperspectral thermal imagers provide rich spectral information, but high data dimensionality and limited onboard resources make real-time processing challenging. As wildfires increase in frequency and severity, the need for low-latency and computationally efficient onboard detection methods is critical. We present a systematic evaluation of multiple deep learning architectures, including custom Convolutional Neural Networks (CNNs) and Transformer-based models, for multi-class fire classification. We also introduce PyroFocus, a two-stage pipeline that performs fire classification followed by fire radiative power (FRP) regression or segmentation to reduce inference time and computational cost for onboard deployment. Using data from NASA's MODIS/ASTER Airborne Simulator (MASTER), which is similar to a next-generation fire detection sensor, we compare accuracy, inference latency, and resource efficiency. Experimental results show that the proposed two-stage pipeline achieves strong trade-offs between speed and accuracy, demonstrating significant potential for real-time edge deployment in future wildfire monitoring missions.