  We use the Fisher matrix formalism and semi-numerical simulations to derive
quantitative predictions of the constraints that power spectrum measurements on
next-generation interferometers, such as the Hydrogen Epoch of Reionization
Array (HERA) and the Square Kilometre Array (SKA), will place on the
characteristics of the X-ray sources that heated the high redshift
intergalactic medium. Incorporating observations between $z=5$ and $z=25$, we
find that the proposed 331 element HERA and SKA phase 1 will be capable of
placing $\lesssim 10\%$ constraints on the spectral properties of these first
X-ray sources, even if one is unable to perform measurements within the
foreground contaminated "wedge" or the FM band. When accounting for the
enhancement in power spectrum amplitude from spin temperature fluctuations, we
find that the observable signatures of reionization extend well beyond the peak
in the power spectrum usually associated with it. We also find that lower
redshift degeneracies between the signatures of heating and reionization
physics lead to errors on reionization parameters that are significantly
greater than previously predicted. Observations over the heating epoch are able
to break these degeneracies and improve our constraints considerably. For these
two reasons, 21\,cm observations during the heating epoch significantly enhance
our understanding of reionization as well.
