This paper introduces a wildfire monitoring system based on a fleet of Unmanned Aerial Vehicles (UAVs) to provide firefighters with precise and up-to-date information about a propagating wildfire, so that they can devise efficient suppression actions. We present an approach to plan trajectories for a fleet of fixed-wing UAVs to observe a wildfire evolving over time by tailoring the Variable Neighborhood Search metaheuristic to the problem characteristics. Realistic models of the terrain, of the fire propagation process, and of the UAVs are exploited, together with a model of the wind, to predict wildfire spread and plan accordingly the UAVs motions. Algorithms and models are integrated within a software architecture allowing tests with real and simulated UAVs flying over synthetic wildfires. Results of a mixed-reality test campaign show the ability of the proposed system to effectively map wildfire propagation.