This article presents a study of the free cooling of a low-energy building using a latent-heat thermal energy storage (LHTES) device integrated into a mechanical ventilation system. The cylindrical LHTES device was filled with spheres of encapsulated RT20 paraffin, a phase-change material (PCM). A numerical model of the LHTES was developed to identify the parameters that have an influence on the LHTES’s thermal response, to determine the optimum phase-change temperature and to form the LHTES’s temperature-response function. The last of these defines the LHTES’s outlet-air temperature for a periodic variation of the inlet ambient-air temperature and the defined operating conditions. The temperature-response function was then integrated into the TRNSYS building thermal response model. Numerical simulations showed that a PCM with a melting temperature between 20 and 22 °C is the most suitable for free cooling in the case of a continental climate. The analyses of the temperatures in a low-energy building showed that free cooling with an LHTES is an effective cooling technique. Suitable thermal comfort conditions in the presented case-study building could be achieved using an LHTES with 6.4 kg of PCM per square metre of floor area.