We present temperature-dependent ionic transport through an array of nanopores (cylindrical and conical) and a single conical nanopore functionalized with amine-terminated poly(N-isopropylacrylamide) [PNIPAAM-NH2] brushes. For this purpose, nanopores are fabricated in heavy ion irradiated polyethylene terephthlate (PET) membranes by a controlled chemical track-etching technique, which leads to the generation of carboxyl (COOH) groups on the pore surface. End-functionalized polymer chains are immobilized onto the inner pore walls via a 'grafting-to' approach through the covalent linkage of surface COOH moieties with the terminal amine groups of the PNIPAAM molecules by using carbodiimide coupling chemistry. The success of the chemical modification reaction is corroborated by measuring the permeation flux of charged analytes across the multipore membranes in an aqueous solution, and for the case of single conical pore by measuring the current-voltage (I-V) characteristics, which are dictated by the electrostatic interaction of the charged pore surface with the mobile ions in an electrolyte solution. The effective nanopore diameter is tuned by manipulating the environmental temperature due to the swelling/shrinking behaviour of polymer brushes attached to the inner nanopore walls, leading to a decrease/increase in the ionic transport across the membrane. This process should permit the thermal gating and controlled release of ionic drug molecules through the nanopores modified with thermoresponsive polymer chains across the membrane.