In Structural Health Monitoring (SHM), the instrumentation policies for buildings usually require large numbers of high-resolution sensors. The relatively high economic cost for the sensors and their interconnecting cables has discouraged the widespread application of SHM. For modal analysis, small number of sensors means low spatial resolution of mode shapes, which limits the possibility of differentiating between close frequency modes in a single measurement and between consecutive measurements on a continuous monitoring system. In this study, we try to overcome this limitation, particularly on the tracking component of SHM, with the aid of a predictive numerical model based on the effect of the ambient temperature on the modal frequency. To validate this hypothesis, we test it on a real building, monitored with a small number of low-resolution sensors. The methodology's performance is evaluated during normal conditions, rainfall and also after the damaging Chile Maule earthquake (Mw of 8.8), proving to be effective for tracking purposes. For this building, the sensitivity of the mode shape and damping to the environment is also studied, showing a very low sensitivity as compared to the frequency. This validates the simpler temperature – frequency model.