When poly(butylene terephthalate) (PBT) is annealed, a second endotherm is often displayed in a subsequent scanning thermal analysis at a temperature below that of the original endotherm, and this new endotherm appears to grow with annealing at the expense of the original. This growth is not due to chemical changes, because the thermogram obtained before annealing is recovered after complete melting. But a physical change would also seem unlikely because the transformation of higher-melting into lower-melting crystals is generally prohibited by thermodynamics. Two hypotheses to explain the result were tested. The first is that higher-melting crystals are not transformed into lower-melting crystals. Instead, because of recrystallization during thermal analysis, the single endotherm that results without annealing overestimates the population of high-melting crystals present before the analysis. This hypothesis was tested by extending to annealing a mathematical analysis previously used to describe the thermal scanning behavior of specimens crystallized at different cooling rates. Though most features of the thermograms obtained after annealing were able to be described, the decrease in the higher-temperature endotherm concomitant with growth of the lower endotherm was not. The second hypothesis is that the transformation of higher-melting to lower-melting crystals during annealing is allowed because it is coupled to the crystallization of formerly amorphous material. The amount of such crystallization observed for PBT was found to be sufficient to satisfy thermodynamic requirements, suggesting that this hypothesis is correct.