The temperature profile in the Heat Affected Zone (HAZ) during induction welding is one of the most important factors determining the weld quality of High-Frequency Induction (HFI) welded steel tubes. In this work, numerical computation of the 3D temperature profile in the steel tube has been done by coupling the electromagnetic model with the thermal model. The high-frequency current and the magnetic fields in the tube, coil and impeder have been evaluated. The resulting power from the induced current is used to evaluate the temperature in the joining edges of the tube. The continuous tube movement has been implemented by considering an additional transport term in the heat equation. The simulations consider non-linear electromagnetic and thermal properties of the steel when it undergoes temperature rise to the welding temperature. The temperature profile from the resulting simulation gives information to control the subsequent process of joining the edges of the steel tube.