  We explore the complete history of the 21-cm signal in the redshift range z =
7-40. This redshift range includes various epochs of cosmic evolution related
to primordial star formation, and should be accessible to existing or planned
low-frequency radio telescopes. We use semi-numerical computational methods to
explore the fluctuation signal over wavenumbers between 0.03 and 1 Mpc$^{-1}$,
accounting for the inhomogeneous backgrounds of Ly-$\alpha$, X-ray,
Lyman-Werner and ionizing radiation. We focus on the recently noted expectation
of heating dominated by a hard X-ray spectrum from high-mass X-ray binaries. We
study the resulting delayed cosmic heating and suppression of gas temperature
fluctuations, allowing for large variations in the minimum halo mass that
contributes to star formation. We show that the wavenumbers at which the
heating peak is detected in observations should tell us about the
characteristic mean free path and spectrum of the emitted photons, thus giving
key clues as to the character of the sources that heated the primordial
Universe. We also consider the line-of-sight anisotropy, which allows
additional information to be extracted from the 21-cm signal. For example, the
heating transition at which the cosmic gas is heated to the temperature of the
cosmic microwave background should be clearly marked by an especially isotropic
power spectrum. More generally, an additional cross-power component $P_X$
directly probes which sources dominate 21-cm fluctuations. In particular,
during cosmic reionization (and after the just-mentioned heating transition),
$P_X$ is negative on scales dominated by ionization fluctuations and positive
on those dominated by temperature fluctuations.
