Many cities are suffering the effects of urban heat islands (UHI) or urban cool islands (UCI) due to rapid urban expansion and numerous infrastructure developments. This paper presents a lumped urban-building thermal coupling model which captures the fundamental physical mechanism for thermal interactions between buildings and their urban environment. The benefits of the model are its simplicity and high computational efficiency for practical use in investigating the diurnal urban air temperature change and its asymmetry in a city with both naturally-ventilated (NV) and air-conditioned (AC) buildings. Our model predicts a lower urban heat island and higher urban cool island intensity in a city with naturally-ventilated buildings than for a city with air-conditioned buildings. During the urban densification (from a low-rise, low-density city to a high-rise, high-density one), the increases in the time constant and internal heat gain give rise to asymmetric warming phenomena, which become more obvious in a city with air-conditioned buildings rather than naturally-ventilated ones. Unlike previous studies, we found that a low-rise, low-density city experiences a stronger urban cool island effect than a high-rise, high-density city due to less heat being emitted into the urban atmosphere. The urban cool/heat island effect will firstly increase/decrease, and then rapidly decrease/increase and ultimately disappear/dominate with increasing time constant in the process of urbanization/urban densification.