Unmanned Aerial Vehicles (UAVs) are expected to transform logistics, reducing delivery time, costs, and emissions. This study addresses an on-demand delivery , in which fleets of UAVs are deployed to fulfil orders that arrive stochastically. Unlike previous work, it considers UAVs with heterogeneous, unknown energy storage capacities and assumes no knowledge of the energy consumption models. We propose a decentralised deployment strategy that combines auction-based task allocation with online learning. Each UAV independently decides whether to bid for orders based on its energy storage charge level, the parcel mass, and delivery distance. Over time, it refines its policy to bid only for orders within its capability. Simulations using realistic UAV energy models reveal that, counter-intuitively, assigning orders to the least confident bidders reduces delivery times and increases the number of successfully fulfilled orders. This strategy is shown to outperform threshold-based methods which require UAVs to exceed specific charge levels at deployment. We propose a variant of the strategy which uses learned policies for forecasting. This enables UAVs with insufficient charge levels to commit to fulfilling orders at specific future times, helping to prioritise early orders. Our work provides new insights into long-term deployment of UAV swarms, highlighting the advantages of decentralised energy-aware decision-making coupled with online learning in real-world dynamic environments.