An energy-conserving analytical solution for heat flow at midocean ridge crests was obtained by assuming that the material accreting at the ridge acts as a known heat source along the ridge axis. Latent heat is included consistently in the adiabatic melting of the ascending mush and in the solidification of the basaltic crust. At spreading rates below about 1 cm/yr, lateral heat conduction away from the ridge precludes the existence of a steady state magma chamber. At higher spreading rates, material cannot cool, since dikes in the lower crust and a magma chamber of some type must exist. If most of the chamber were filled with mush, the chamber would be more mechanically stable than one filled with molten magma. It is most probable that new material from below ascends to the top of the magma and then either further ascends as a dike or spreads laterally along the top of the chamber. If crystal settling is important and accretion of material to the roof is minor, the magma chamber will be flat topped and will extend far enough laterally that incoming material will cool to a mostly crystalline cumulate mush. The geothermal calculations and kinematic models are testable from geologic observations on ophiolitic complexes and by planned drilling. It appears that the spreading rate of fossil ridges can be determined from these considerations.