This work proposes a learnheuristic approach (combination of heuristics with machine learning) to solve an aerial-drone team orienteering problem. The goal is to maximise the total reward collected from information gathering or surveillance observations of a set of known targets within a fixed amount of time. The aerial drone team orienteering problem has the complicating feature that the travel times between targets depend on a drone's flight path between previous targets. This path-dependence is caused by the aerial surveillance drones flying under the influence of air-resistance, gravity, and the laws of motion. Sharp turns slow drones down and the angle of ascent and air-resistance influence the acceleration a drone is capable of. The route dependence of inter-target travel times motivates the consideration of a learnheuristic approach, in which the prediction of travel times is outsourced to a machine learning algorithm. This work proposes an instance-based learning algorithm with interpolated predictions as the learning module. We show that a learnheuristic approach can lead to higher quality solutions in a shorter amount of time than those generated from an equivalent metaheuristic algorithm, an effect attributed to the search-diversity enhancing consequence of the online learning process.