In this work, we consider the problem of multi-agent informative path planning (IPP) for robots whose sensor visibility continuously changes as a consequence of a time-varying natural phenomenon. We leverage ergodic trajectory optimization (ETO), which generates paths such that the amount of time an agent spends in an area is proportional to the expected information in that area. We focus specifically on the problem of multi-agent drone search of a wildfire, where we use the time-varying environmental process of smoke diffusion to construct a sensor visibility model. This sensor visibility model is used to repeatedly calculate an expected information distribution (EID) to be used in the ETO algorithm. Our experiments show that our exploration method achieves improved information gathering over both baseline search methods and naive ergodic search formulations.