This work deals with the problem of predicting the temperature-dependent equivalent elastic properties of cork-based composites by investigating the influence of the variability related to the material properties of natural cork. A dedicated numerical homogenisation approach based on the strain energy of periodic and a-periodic media has been developed to this purpose. The proposed methodology is based, on the one hand, on an efficient modelling strategy capable to generate 2D and 3D finite element models which closely emulates the realistic meso-structure of the agglomerate. On the other hand, the strategy makes use of the Monte Carlo algorithm to study the influence of the variability in model inputs on the equivalent elastic behaviour of the cork-based composite at different temperatures. Firstly, the effectiveness of the modelling strategy in representing a realistic meso-structure of the agglomerate, in terms of geometry, has been evaluated by comparing the numerical results to digital images of real cork-based composites. Secondly, the homogenisation strategy has been applied to a realistic configuration of cork agglomerate. Numerical results show that the greater the temperature the lower the overall stiffness of the agglomerate, according to natural cork trends, but the variability related to the macroscopic equivalent elastic properties of the agglomerate is considerably lower than that affecting the elastic behaviour of the natural cork, which represents a positive result concerning the use of cork agglomerates in industrial applications.