The invention relates to use of polylactide (PLA) as an extruded polymer coating on paper or board intended for the production of containers and packages, which are heated in a stove or microwave oven. According to the invention a polyfunctional cross-linking agent, such as trialkyl isocyanurate (TAIC), is blended with PLA, and the extruded coating layer is subjected to cross-linking electron beam (EB) radiation. PLA may be used as such or blended with another biodegradable polyester such as polybutylene succinate (PBS). EB radiation has been found to improve adhesion of the coating to the paper or board substrate, heat-scalability of the coating, and heat-resistance of the finished containers and packages.