We have obtained a two-dimensional electron-solid phase diagram in the extreme magnetic quantum limit by studying the temperature dependence of the radiative recombination of electrons in a GaAs/AlxGa1-xAs heterojunction with holes bound to a delta-layer, 250 A away in the GaAs, of Be acceptors. The low-energy shoulder to the luminescence line, indicating the presence of the electron solid, is seen to disappear at a filling-factor-dependent critical temperature. We observe no shoulder above a filling factor of 0.25, and the critical temperature falls to below 0.4 K at filling factors 1/5 and 1/7.