Koopman mode decomposition (KMD) is a technique of nonlinear time-series analysis capable of decomposing data on complex spatio temporal dynamics into multiple modes oscillating with single frequencies, called the Koopman modes (KMs). We apply KMD to measurement data on oscillatory dynamics of a temperature field inside a room that is a complex phenomenon ubiquitous in our daily lives and has a clear technological motivation in energy-efficient air conditioning. To characterize not only the oscillatory field (scalar field) but also associated heat flux (vector field), we introduce the notion of a temperature gradient using the spatial gradient of a KM. By estimating the temperature gradient directly from data, we show that KMD is capable of extracting a distinct structure of the heat flux embedded in the oscillatory temperature field, relevant in terms of air conditioning.