Disclosed is a smoking article containing a rod containing a smokable composition, an optional wrapper for the rod, and at least one polymer or oligomer comprising monomer units of a polycarboxylic acid ester disposed on or in the rod, the wrapper, or both. The polycarboxylic acid ester contains an acid moiety having at least two carboxylic groups, and at least two alcohol moieties independently selected from those corresponding to a cycloalkyl alcohol or an aryl alcohol. The cycloalkyl alcohol or aryl alcohol is a flavorant, or chemesthetic agent, or both. In addition, a method for the controlled release of these flavorant or chemesthetic agents is described, which comprises pyrolyzing at least one polymer or oligomer.