We present a mathematical model to diagnose HVAC systems in buildings based upon the analysis of a small number of ambient state variables. In particular, the equations of the model accurately fit recorded data of temperature, relative humidity and carbon dioxide concentration in different workplaces. For validation, data were obtained under different conditions and with different sensors. In particular, we designed and fabricated a wireless sensor that measures and transmits data to a remote device and we also, applied our model to data collected using a commercial sensor. For each case, information was obtained that could be used to understand and predict the evolution of ambient variables that impact thermal comfort and energy consumption in buildings. The tools presented here can thus be of great interest to achieve affordable, smart energy-efficient buildings, while adhering to environmental laws and comfort for work spaces. (C) 2016 Elsevier Ltd. All rights reserved.