Researchers, policy makers, and engineers need to make sense of data on spreading processes as diverse as viral infections, water contamination, and misinformation in social networks. Classical questions include predicting infection behavior in a given network or deducing the structure of a network from infection data. We study two central problems in this area. In graph discovery, we aim to fully reconstruct the structure of a graph from infection data. In source detection, we observe a limited subset of the infections and aim to deduce the source of the infection chain. These questions have received considerable attention and have been analyzed in many settings (e.g., under different models of spreading processes), yet all previous work shares the assumption that the network has the same structure at every point in time. For example, if we consider how a disease spreads, it is unrealistic to assume that two people can either never or always infect each other, rather such an infection is possible precisely when they meet. Temporal graphs, in which connections change over time, have recently been used as a more realistic graph model to study infections. Despite this recent attention, we are the first to study graph discovery or source detection in temporal graphs. We propose models for temporal graph discovery and source detection that are consistent with previous work on static graphs and extend it to embrace the stronger expressiveness of temporal graphs. For this, we employ the standard susceptible-infected-resistant model of spreading processes, which is particularly often used to study diseases. We provide algorithms, lower bounds, and some experimental evaluation.