The core-peripheral temperature difference (CPTD) refers to the difference between the body's core temperature (e.g., chest or abdomen) and peripheral skin temperature (e.g., hands or feet). It serves as a key biomarker for assessing the hemodynamic status of newborns and is an important early warning indicator of potential shock and severe infection. Measurement of CPTD in clinical practice currently requires the use of an infrared spot thermometer to measure the temperature of multiple body parts of a neonate, which is not possible for continuous and fully automatic long-term monitoring. To address these limitations, we propose a thermal infrared (TIR)-based approach that enables non-contact, fully automatic, and continuous CPTD measurement for neonates. The spatial redundancy property of TIR is utilised and combined with a deep learning-based body parsing model to automatically detect different body parts of a neonate, including the chest and limbs (e.g., hand or foot), and measure the temperatures of these two parts to derive their difference as CPTD. Although accurate measurement of the absolute temperature of the neonatal skin is difficult due to the calibration of the TIR camera and environmental influence, the temperature difference between different body parts that emphasizes the spatial contrast at certain moments can be reliably estimated, and it is independent of the subject and environment. In a prospective clinical trial involving 40 preterm infants, our TIR-based CPTD measurement showed a mean absolute error less than