This paper demonstrates and systematically characterizes the enrichment of biomolecular compounds using aptamer-functionalized surfaces within a microfluidic device. The device consists of a microchamber packed with aptamer-functionalized microbeads and integrated with a microheater and temperature sensor to enable thermally controlled binding and release of biomolecules by the aptamer. We first present an equilibrium binding-based analytical model to understand the enrichment process. The characteristics of the aptamer-analyte binding and enrichment are then experimentally studied, using adenosine monophosphate (AMP) and a specific RNA aptamer as a model system. The temporal process of AMP binding to the aptamer is found to be primarily determined by the aptamer-AMP binding kinetics. The temporal process of aptamer-AMP dissociation at varying temperatures is also obtained and observed to occur relatively rapidly (< 2 s). The specificity of the enrichment is next confirmed by performing selective enrichment of AMP from a sample containing biomolecular impurities. Finally, we investigate the enrichment of AMP by either discrete or continuous introduction of a dilute sample into the microchamber, demonstrating enrichment factors ranging from 566 to 686×, which agree with predictions of the analytical model.