Systems and methods are provided for controlling welding. One embodiment is a method for controlling welding of a composite part. The method includes locating a linear fiber optic sensor along a composite part comprising a matrix of thermoplastic reinforced by fibers, measuring temperatures along the weld line via the linear fiber optic sensor, performing induction welding at the composite part along the weld line, determining a continuum of weld temperatures along the weld line, and controlling the induction welding based on the continuum of weld temperatures.