A new tool for infra-red thermographic inversion on Tokamak Energy's spherical tokamak, ST40, is developed in-house and here presented. Functional Analysis of Heat Flux (FAHF) is written in Python, and configured for multi-2D thermographic inversions, solving the heat conduction equation within the divertor tiles via the finite difference method, and leveraging an explicit time-marching scheme. Using infra-red camera data of the highest effective spatial resolution available, FAHF ultimately outputs the plasma perpendicular heat flux on the divertor, crucial quantity in any edge plasma investigation. In the present work, the internal numerics of the tool is first successfully verified by formal time and space convergence analyses, and corroborated by an energy balance assessment. A significant sensitivity of the perpendicular heat flux computed by FAHF to the user-selected spatial resolution is then evidenced. However, a precise heat flux is proved to be recoverable by ensuring a sufficiently high resolution. Last, the appropriateness of the model/geometry simplifications adopted in FAHF is successfully confirmed, by means of comparison against COMSOL Multiphysics simulations. FAHF is hence conclusively proven to qualify as a precise and accurate tool for infra-red thermographic inversions.