We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion and Monte Carlo simulations to characterise the order-by-disorder transition. By direct evaluation of the density of states we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in $2d$ and $3d$ samples, and evaluate how anomalous finite-size effects could be exploited to detect this phenomenon experimentally in two-dimensional artificial systems, or in antiferromagnetic all-in--all-out pyrochlores like Nd$_2$Hf$_2$O$_7$ or Nd$_2$Zr$_2$O$_7$, for the first time.
Comment: 5 pages, 3 figures + supplemental material