The relaxation process of shear-induced crystal nucleation precursors has been investigated in a temperature range slightly above the melting point using a series of commercial grade isotactic poly(1-butene)s with different molecular weights. Development of transcrystalline morphology from the surface of a fiber pulled through the molten polymer is ascribed to high concentration of ordered clusters promoted by the alignment of chain segments under the high-intensity shear flow at the fiber-melt interface. Sheared melts isothermally crystallized immediately after cessation of flow exhibit a well-pronounced cylindritic morphology, characterized by closely spaced fibrillar branches; on the other hand, prolonged relaxation in the molten state before crystallization leads to classical spherulitic morphology. The lifetime of shear-induced nucleation precursors, t*, has been associated with the complete disappearance of the transcrystalline morphology. It has been found that systems composed of short chains relax much faster than those containing a large fraction of high molecular weight species. When relaxed slightly above the melting point of the tetragonal crystal modification the highest molecular weight samples keep memory of flow-induced structuring during several hours. Temperature has a dominant role on the kinetics of reequilibration of sheared samples: experimental data of t* obtained in wide range of "relaxation" temperatures can be fitted by an Arrhenius-type equation with an apparent activation energy of around 700 kJ/mol. Results can be justified by considering a network of aligned and ordered polymolecular clusters, originated under the high-intensity shear flow field at the solid-melt interface, whose relaxation involves large scale restructuring.