In the differential scanning calorimetry (DSC) scans of the annealed states of vapor-deposited, hyperquenched, and crystal-amorphized solids, the glass-softening or T-g endotherm is interrupted by the crystallization exotherm, thus making the T-g endotherm appear like a rounded peak. This apparent peak is occasionally misidentified as a sub-T-g peak, which appears in the 0.7T(g) to 0.8T(g) range in the DSC scan of glasses preannealed at a specific temperature, T-ann. To help prevent such misidentification, we provide four criteria for distinguishing the apparent peak of the T-g endotherm from a sub-T-g peak: (i) Crystallization occurs in the T-g endotherm range or at T just above it, and not in the sub-T-g peak range. (ii) The T-g endotherm onset occurs at T > T-ann, but the sub-T-g peak onset occurs at T-ann. (iii) Unannealed glasses show a T-g endotherm; only preannealed glasses show the sub-T-g peak, and the height of the sub-T-g peak and its area vary when T-ann and the annealing time are varied. (iv) Slope of the DSC scan may decrease, become zero or become negative prior to the onset of the T-g endotherm, but it does not decrease and remains positive prior to the onset of sub-T-g peak. The annealed state of hyperquenched glassy water is known to crystallize in the 142-150 K range of its endotherm, the onset temperature of the endotherm is higher than T-ann, its unannealed state shows the T-g endotherm, and the slope of the scan prior to the onset temperature is not always positive. These observations remove the basis for a recent conjecture that the T-g of water is between 165 and 180 K, and is unobservable. Available calorimetric data on vapor-deposited, hyperquenched, and mechanically amorphized solids have shown a T-g endotherm partially superposed by the crystallization exotherm, but T-g itself does not change. It is proposed that intermediate states formed during the occurrence of disorder-order transitions in solids and in proteins can be studied in the time domain by using their hyperquenched glassy and mechanically amorphized states.