Measuring wildland fire behaviour is essential for fire science and fire management. Aerial thermal infrared (TIR) imaging provides outstanding opportunities to acquire such information remotely. Variables such as fire rate of spread (ROS), fire radiative power (FRP) and fire line intensity may be measured explicitly both in time and space, providing the necessary data to study the response of fire behaviour to weather, vegetation, topography and firefighting efforts. However, raw TIR imagery acquired by Unmanned Aerial Vehicles (UAVs) requires stabilization and georeferencing before any other processing can be performed. Aerial video usually suffers from instabilities produced by sensor movement. This problem is especially acute near an active wildfire due to fire-generated turbulence. Furthermore, the nature of fire TIR video presents some specific challenges that hinder robust inter-frame registration. Therefore, this paper presents a software-based video stabilization algorithm specifically designed for thermal infrared imagery of forest fires. After a comparative analysis of existing image registration algorithms, the KAZE feature-matching method was selected and accompanied by pre-and post-processing modules. These included foreground histogram equalization and a multireference framework designed to increase the algorithm's robustness in the presence of missing or faulty frames. Performance of the proposed algorithm was validated in a total of nine video sequences acquired during field fire experiments. The proposed algorithm yielded a registration accuracy between 10 and 1000 times higher than other tested methods, returned 10x more meaningful feature matches and proved robust in the presence of faulty video frames. The ability to automatically cancel camera movement for every frame in a video sequence solves a key limitation in data processing pipelines and opens the door to a number of systematic fire behaviour experimental analyses. Moreover, a completely automated process supports the development of decision support tools that can operate in real time during an emergency.