Cardiovascular disease, the leading cause of death globally, is an age-related disease. Understanding the morphological and functional changes of the heart during ageing is a key scientific question, the answer to which will help us define important risk factors of cardiovascular disease and monitor disease progression. In this work, we propose a novel conditional generative model to describe the changes of 3D anatomy of the heart during ageing. The proposed model is flexible and allows integration of multiple clinical factors (e.g. age, gender) into the generating process. We train the model on a large-scale cross-sectional dataset of cardiac anatomies and evaluate on both cross-sectional and longitudinal datasets. The model demonstrates excellent performance in predicting the longitudinal evolution of the ageing heart and modelling its data distribution.