An ideal naturally ventilated building model that allows a theoretical study of the effect of thermal mass associating with the non-linear coupling between the airflow rate and the indoor air temperature is proposed. When the ventilation rate is constant, both the phase shift and fluctuation of the indoor temperature are determined by the time constant of the system and the dimensionless convective heat transfer number. When the ventilation rate is a function of indoor and outdoor air temperature difference, the thermal mass number and the convective heat transfer air change parameter are suggested. The new thermal mass number measures the capacity of heat storage, rather than the amount of thermal mass. The analyses and numerical results show that the non-linearity of the system does neither change the periodic behaviour of the system, nor the behaviour of phase shift of the indoor air temperature when a periodic outdoor air temperature profile is considered. The maximum indoor air temperature phase shift induced by the direct outdoor air supply without control is 6 h.