Phylogenetic methods can use the sampling times of molecular sequence data to calibrate the molecular clock, enabling the estimation of evolutionary rates and timescales for rapidly evolving pathogens and data sets containing ancient DNA samples. A key aspect of such calibrations is whether a sufficient amount of molecular evolution has occurred over the sampling time window, that is, whether the data can be treated as having come from a measurably evolving population. Here, we investigate the performance of a fully Bayesian evaluation of temporal signal (BETS) in sequence data. The method involves comparing the fit to the data of two models: a model in which the data are accompanied by the actual (heterochronous) sampling times, and a model in which the samples are constrained to be contemporaneous (isochronous). We conducted simulations under a wide range of conditions to demonstrate that BETS accurately classifies data sets according to whether they contain temporal signal or not, even when there is substantial among-lineage rate variation. We explore the behavior of this classification in analyses of five empirical data sets: modern samples of A/H1N1 influenza virus, the bacterium Bordetella pertussis, coronaviruses from mammalian hosts, ancient DNA from Hepatitis B virus, and mitochondrial genomes of dog species. Our results indicate that BETS is an effective alternative to other tests of temporal signal. In particular, this method has the key advantage of allowing a coherent assessment of the entire model, including the molecular clock and tree prior which are essential aspects of Bayesian phylodynamic analyses.