It is known that most multi-component glasses cold-crystallize incongruently on heating through the temperature range of their ultraviscous melt. If the incongruent melt's composition changes with time, its viscosity, eta, and the glass-liquid transition temperature, T-g, would change. Since the eta, relaxation time, and expansion coefficient of a liquid in its partially crystallized mixture cannot be determined, we used scanning calorimetry to study the liquid-glass-liquid transition during thermal cycling of the incongruently crystallizing Ce66Al10Cu20Co4 glass. Its T-g is 358 K for 20 K/min and 354 K for 10 K/min heating rates, and its ultraviscous melt crystallized incongruently when heated beyond the hysteresis peak of its heat capacity scan. Its sample that had been aged for nine years at ambient conditions had a higher crystallization-onset temperature than an un-aged sample. Delayed enthalpy gain on heating of the aged glass is similar to 1/5th of the enthalpy lost on its crystallization. Crystallization of the melt occurred on both the heating and cooling paths of a thermal cycle and T-g of the un-aged glass increased as the volume fraction of the compositionally different glass, f(gl), decreased. The increase was by 8K after the 24th cycle of 20 K/min, and by 11 K after the 13th cycle of 10 K/min cooling-heating. The highest T-g values reached differed by similar to 1 K, which indicates that closely similar TgS may be reached if the total time period for thermal cycling (at different rates) is kept the same. As f(gl) approached its limiting low value, increase in Tg per cycle itself increased, and the T-g-endotherm became unusually broad, which we attribute to diverse energies of interactions between the incongruent liquid and the crystal-surface atoms that dominate at the lowest f(gl). (C) 2015 Elsevier B.V. All rights reserved.