The present work deals with the new measurement of the thermal slip coefficient in an original manner, that is by correlating the thermal slip coefficient to a mass flow rate that is engendered by solely applying a known inequality of temperature along a solid surface at contact with the fluid. As far as we are aware, these are the first experimental results of the thermal slip coefficient obtained from a temperature gradient induced mass flow rate (thermal transpiration). The thermal slip coefficients were obtained for argon and nitrogen by submitting a single glass capillary to small temperature differences, that is DT ¼ 71, 53.5 and 37 K for the following condition DT (T av. In the frame of Maxwell's diffuse specular kernel an accommodation coefficient is associated to the obtained thermal slip coefficient. The here obtained values of the accommodation coefficient are similar to those which have been previously found from the isothermal mass flow rate measurements.