Display omitted •Natural frequency tracking is newly applied for SHM of a stiff masonry Palace.•An effective tracking of natural frequencies and crack amplitudes is achieved.•Frequency-temperature correlations are negative in sign due to a major crack pattern.•Crack amplitudes as predictors enhance statistical modeling of natural frequencies.•Remarkable freezing effects on natural frequencies are highlighted. In recent years, the development of long-term structural health monitoring systems for preventive conservation of historic monumental buildings is receiving a growing trend of scientific interest. Nevertheless, the damage detection effectiveness of these systems is still debated, especially in respect to complex masonry palaces where both local and global failure mechanisms can be activated, whereby the majority of the documented successful applications are limited to masonry towers. In particular, one major issue that needs to be solved in order to derive damage sensitive features is associated to the removal of the effects of changes in environmental conditions and, primarily, of ambient temperature, from static and dynamic signatures. This paper aims to contribute to improving knowledge in this field, by investigating temperature effects on static and dynamic response of an iconic Italian monumental palace: the Consoli Palace in Gubbio. With the purpose of early detecting earthquake-induced damages, as well as damages caused by material degradation associated to awkward environmental conditions, a simple low-cost mixed static and dynamic long-term structural health monitoring system has been installed on the Palace by the authors in July 2017. After discussing surveys, ambient vibration tests, diagnostic investigations, numerical modeling and model calibration of the Palace, the analysis of the first year of monitoring data is presented. This analysis shows that, differently from what observed in other literature works on historic masonry towers, the natural frequencies of the Palace show a marked and sometimes non-linear decreasing trend with increasing ambient temperature, that can be effectively removed through linear statistical filtering provided that dynamic regression models, using past values of predictors, are used. On the other side, the evolution of the amplitudes of two major cracks monitored within the building also shows a marked linear decreasing trend with increasing ambient temperature. These results are meaningful towards the use of monitoring data for assessing the initial health conditions of a structure, as well as in a damage detection perspective.