Summary: Techniques associated with temperature control and measurement in quench furnaces are described and a study made of calibration problems. Systematic temperature errors as great as 30°C in published results from separate laboratories are explicable. A comprehensive redetermination of temperatures of invariant equilibria in systems containing CaO, MgO, Al₂O₃, SiO₂, Na₂O, Fe-O₂, has been initiated and the results to date are presented, including approximate determinations of three invariant equilibria in the system CaO-MgO-Al₂O₃-SiO₂ involving liquid, monticellite, spinel, and two of merwinite, periclase, and forsterite, which are important in the melting of magnesia refractories, and precise determinations of the three newly recognized invariant equilibria involving liquid, spinel, diopside, and two of forsterite, melilite, and anorthite.