  We present analysis of the normalised 21-cm bispectrum from fully-numerical
simulations of intergalactic-medium heating by stellar sources and high-mass
X-ray binaries (HMXB) during the cosmic dawn. Lyman-$\alpha$ coupling is
assumed to be saturated, we therefore probe the nature of non-Gaussianities
produced by X-ray heating processes. We find the evolution of the normalised
bispectrum to be very different from that of the power spectrum. It exhibits a
turnover whose peak moves from large to small scales with decreasing redshift,
and corresponds to the typical separation of emission regions. This
characteristic scale reduces as more and more regions move into emission with
time. Ultimately, small-scale fluctuations within heated regions come to
dominate the normalised bispectrum, which at the end of the simulation is
almost entirely driven by fluctuations in the density field. To establish how
generic the qualitative evolution of the normalised bispectrum we see in the
stellar + HMXB simulation is, we examine several other simulations - two
fully-numerical simulations that include QSO sources, and two with contrasting
source properties produced with the semi-numerical simulation 21cmFAST. We find
the qualitative evolution of the normalised bispectrum during X-ray heating to
be generic, unless the sources of X-rays are, as with QSOs, less numerous and
so exhibit more distinct isolated heated profiles. Assuming mitigation of
foreground and instrumental effects are ultimately effective, we find that we
should be sensitive to the normalised bispectrum during the epoch of heating,
so long as the spin temperature has not saturated by $z \approx 19$.
