A temperature jump boundary condition for a slip flow in a micro-channel with the constant wall temperature is widely used for a boundary condition of an energy equation. It is well known that a sliding shear work should be included in the slip boundary when the energy equation includes the viscous dissipation and the substantial derivative of pressure terms. However, the temperature jump boundary condition does not have the sliding shear work apparently. The temperature jump boundary condition for a case where the energy equation has the both two terms, is verified by obtaining the analytical solution in the fully developed region of a slip flow in a circular tube. And some numerical results are demonstrated.