We study network centrality measures that take into account the specific structure of networks with time-stamped edges. In particular, we explore how such measures can be used to identify nodes most relevant for the spread of epidemics on directed, temporal contact networks. We present a percolation study on the French cattle trade network, proving that time-aware centrality measures such as the TempoRank significantly outperform measures defined on the static network. In order to make TempoRank amenable to large-scale networks, we show how it can be efficiently computed through direct simulation of time-respecting random walks.