We develop and analyze the arguments that giant impact scenarios of lunar origin appear to require an initially hot Moon (near or above the solidus for most of the mass). Pre-giant-impact heating, impact heating, disk evolution heating and cooling, and the accretion of the Moon are all taken into account. However, the current poor understanding of the dynamical continuum disk phase that is expected to intervene between the endpoint of standard giant impact simulations (Cameron et al.) and the beginning of lunatesimal aggregation scenarios (Canup and coworkers), together with other uncertainties, prevent precise conclusions for initial lunar temperatures. Isotopic considerations (especially potassium) do not argue against extensive devolatilization during lunar formation. We also assess the geological and geochemical evidence suggesting that a substantial fraction of the initial Moon was cold (~ 1000 K or less). These arguments are difficult to quantify with high certainty for several reasons, especially the uncertain mechanical properties of the near-surface materials. We conclude that the current uncertainties prevent a firm conclusion about possible conflict between the giant impact scenario and lunar history. However, the bulk of the evidence and modeling suggests hot (near solidus or above) initial conditions for nearly all the lunar mass.