This paper develops a multi-agent heterogeneous search approach that leverages the sensing and motion capabilities of different agents to improve search performance (i.e., decrease search time and increase coverage efficiency). To do so, we build upon recent results in ergodic coverage methods for homogeneous teams, where the search paths of the agents are optimized so they spend time in regions proportionate to the expected likelihood of finding targets, while still covering the whole domain, thus balancing exploration and exploitation. This paper introduces a new method to extend ergodic coverage to teams of heterogeneous agents with varied sensing and motion capabilities. Specifically, we investigate methods of leveraging the spectral decomposition of a target information distribution to efficiently assign available agents to different regions of the domain and best match the agents’ capabilities to the scale at which information needs to be searched for in these regions. Our numerical results show that distributing and assigning coverage responsibilities to agents based on their dynamic sensing capabilities leads to approximately 40% improvement with regard to a standard coverage metric (ergodicity) and a 15% improvement in time to search over a baseline approach that jointly plans search paths for all agents, averaged over 500 randomized experiments.