In engineering planning practice, building simulation is becoming increasingly crucial for evaluating buildings' energetic and thermal behaviour. The appropriate application in the form of models that represent reality precisely, therefore, faces the challenge of realistic parameter specification for uncertain BES model properties. Many of them can only be restricted to a probable range of values. Additional knowledge can be obtained for the case of available measurement data via inverse modelling. This approach minimises cost function values representing discrepancies between associated time series (measured and simulated data sets). Much research has been published in this field for energy consumption characteristics. These approaches differ in several aspects from measured continuous physical state quantities. This article applies general cost indices to air temperature measurement series. For isolated effects such as time delay and amplitude attenuation, the impact on the characteristic values is examined, and their response is evaluated. This survey leads to the conclusion that there is no single parameter suitable for identifying all effects, and a combination is recommended. A new proposal is made for such a combined statistical index, and exemplary applied for measured temperature curves from a castle near Potsdam.