The annealing of three (001) twist grain boundaries in silicon, Σ25, Σ5, and Σ29 has been simulated over a range of temperatures up to the melting point. In contrast to earlier work the ground-state structures of all our boundaries at absolute zero are ordered and comprise well-defined structural units. We found that the boundaries display some degree of structural order at all temperatures up to the melting point. The state of structural order is time-dependent involving fluctuations between different local states of order. In the large angle boundaries (Σ5 and Σ29) we found a continuous disordering transition resulting in complete disorder, and a possibly unbounded interfacial width, only at the bulk melting point. For the small angle Σ25 boundary the width remained finite at all temperatures up to the bulk melting point, and the degree of order was greater than for the large angle boundaries. The quantification of these results has been made possible by the use of an existing bond orientational order parameter, and new techniques introduced here to identify structural units in dynamic boundary structures.