Physical adsorption of gas molecules in microporous materials is an exothermic process, with desorption entropy driving a decrease in uptake with temperature. Enhanced gas sorption with increasing temperature is rare in porous materials and is indicative of sorbate initiated structural change. Here, sorption of C2H6, C3H6, and C3H8 in a flexible microporous metal-organic framework (MOF) {Cu(FPBDC)]·DMF}n (NKU-FlexMOF-1) (H2FPBDC = 5-(5-fluoropyridin-3-yl)-1,3-benzenedicarboxylic acid) that increases with rising temperature over a practically useful temperature and pressure range is reported along with other small molecule and hydrocarbon sorption isotherms. Single X-ray diffraction studies, temperature-dependent gas sorption isotherms, in situ and variable temperature powder X-ray diffraction experiments, and electronic structure calculations were performed to characterize the conformation-dependent sorption behavior in NKU-FlexMOF-1. In total, the data supports that the atypical sorption behavior is a result of loading-dependent structural changes in the flexible framework of NKU-FlexMOF-1 induced by sorbate-specific guest-framework interactions. The sorbates cause subtle adaptations of the framework distinct to each sorbate providing an induced-fit separation mechanism to resolve chemically similar hydrocarbons through highly specific sorbate-sorbent interactions. The relevant intermolecular contacts are shown to be predominantly repulsion and dispersion interactions. NKU-FlexMOF-1 is also found to be stable in aqueous solutions including toleration of pH changes. These experiments demonstrate the potential of this flexible microporous MOF for cost and energy efficient industrial hydrocarbon separation and purification processes. The efficacy for the separation of C3H6/C3H8 mixtures is explicitly demonstrated using NKU-FlexMOF-1a (i.e., activated NKU-FlexMOF-1) for a particular useful temperature range.