In the present work, a capillary dielectric-barrier discharge of the coaxial electrode configuration, commonly employed to atmospheric-pressure cold plasma jet production, is studied in terms of thermal effects. The discharge is driven by sinusoidal high voltage in the kHz range and operates with helium gas channeled into a capillary dielectric tube having one end opened to the atmospheric air. The voltage amplitude and frequency, gas flow rate, and discharge volume are varied independently, and thermal effects are investigated by experimentally acquired results coupled with numerically determined data. The experiments refer to electrical power measurements, time-resolved temperature measurements, infrared imaging, and high resolution optical emission spectroscopy. The numerical modelling incorporates an electro-hydrodynamic force in the governing equations to take into account the helium-air interplay and uses conjugate heat transfer analysis. The comparison between experimental and numerical data shows that power is principally consumed in the dielectric barrier-helium interface resulting in the dielectric heating. A linear relation between steady state temperatures and supplied power, independent of the designing and operating conditions, is experimentally established. However, the gas flow rate affects the thermal effects differently compared to the other parameters, supporting the idea of a twofold nature of these systems, i.e., electrical and hydrodynamic. The main claim states the possibility of correlating (both experimentally and numerically) designing and operating parameters for evaluating heat distribution and gas temperature in capillary dielectric-barrier discharges used for plasma jet production. This is of high importance for processing temperature-sensitive materials, including bio-specimens.