  A precise test of the theory of stellar evolution can be performed by
measuring the average difference in energy between the neutrino line produced
by ${\rm ^7Be}$ electron capture in the solar interior and the corresponding
neutrino line produced in a terrestrial laboratory. This energy shift is
calculated to be 1.29~keV (to an accuracy of a few percent) for the dominant
ground-state to ground-state transition. The energy shift is approximately
equal to the average temperature of the solar core, computed by integrating the
temperature over the solar interior with a weighting factor equal to the
locally-produced $^7$Be neutrino emission. The characteristic modulation of the
${\rm ^7Be}$ line shape that would be caused by either vacuum neutrino
oscillations or by matter-enhanced (MSW) neutrino oscillations is shown to be
small. Other frequently-discussed weak interaction solutions to the solar
neutrino problem are also not expected to change significantly the line
profile. Therefore, a measurement of the energy shift is a measurement of the
central temperature distribution of the sun.
