Multi-wavelength observations in the sub-mm regime provide information on the distribution of both the dust column density and the effective dust temperature in molecular clouds. In this study, we created high-resolution and high-dynamic-range maps of the Pipe nebula region and explored the value of dust-temperature measurements in particular towards the dense cores embedded in the cloud. The maps are based on data from the Herschel and Planck satellites, and calibrated with a near-infrared extinction map based on 2MASS observations. We have considered a sample of previously defined cores and found that the majority of core regions contain at least one local temperature minimum. Moreover, we observed an anti-correlation between column density and temperature. The slope of this anti-correlation is dependent on the region boundaries and can be used as a metric to distinguish dense from diffuse areas in the cloud if systematic effects are addressed appropriately. Employing dust-temperature data thus allows us to draw conclusions on the thermodynamically dominant processes in this sample of cores: external heating by the interstellar radiation field and shielding by the surrounding medium. In addition, we have taken a first step towards a physically motivated core definition by recognising that the column-density-temperature anti-correlation is sensitive to the core boundaries. Dust-temperature maps therefore clearly contain valuable information about the physical state of the observed medium.