Abstract Microwave polyesterification of trans ‐aconitic acid and ethylene glycol was carried out by controlling two parameters: temperature and exposure to irradiation. A series of crosslinked materials was obtained showing diverse behavior in terms of solubility, glass transition temperature and decomposition temperature. In contrast to heating by convection that could last hours, polyesters obtained by microwave irradiation were obtained after a maximum of 30 min of reaction. More importantly, the polyesterifications were carried out in bulk, with no solvent involved and without the use of any catalyst. © 2020 Society of Chemical Industry