Cross-correlating 21 cm with known cosmic signals will be invaluable proof of the cosmic origin of the first 21-cm detections. As some of the widest fields available, comprising thousands of sources with reasonably known redshifts, narrow-band Lyman-alpha emitter (LAE) surveys are an obvious choice for such cross-correlation. Here, we revisit the 21-cm-LAE cross-correlation, relaxing the common assumption of reionization occurring in a pre-heated intergalactic medium (IGM). Using specifications from the Square Kilometre Array and the Subaru Hyper Supreme-Cam, we present new forecasts of the 21-cm-LAE cross-correlation function at z similar to 7. We sample a broad parameter space of the mean IGM neutral fraction and spin temperature, ((x) over bar (HI), (T) over bar (s)). The sign of the cross-correlation roughly follows the sign of the 21-cm signal: Ionized regions that surround LAEs correspond to relative hot spots in the 21-cm signal when the neutral IGM is colder than the CMB, and relative cold spots when the neutral IGM is hotter than the CMB. The amplitude of the cross-correlation function generally increases with increasing (x) over bar (HI), following the increasing bias of the cosmic H II regions. As is the case for 21 cm, the strongest cross signal occurs when the IGM is colder than the CMB, providing a large contrast between the neutral regions and the ionized regions, which host LAEs. We also vary the topology of reionization and the epoch of X-ray heating. The cross-correlation during the first half of reionization is sensitive to these topologies, and could thus be used to constrain them.
