Smart hydrogel materials are a popular topic of investigation because they have the potential to be used as smart drug carriers and soft actuators. Hydrogel materials showing responsiveness to logic gate-type stimuli are of special interest because their responsiveness can be regulated more accurately than that of common stimuli-responsive materials. In this study, poly(N-isopropylacrylamide) nanogels containing catechol substituents in their polymer network structure were prepared via precipitation polymerization. The prepared nanogels showed AND-type logic gate thermal aggregation behavior. The possible use of this logic gate-type smart nanogel aggregating system was investigated in a smart valve system.