The O.P. has misidentified the thermal fuse location. In the first photo there is a black heatshrink covered object the size and shape of an axial thermal fuse, cable-tied to one of the stator windings. The ceramic, probably sand-filled, 1.6A Time-lag axial fuse isn't in thermal contact with the windings, and has what appears to be a factory original crimp on both leads so is most likely what it is and is solely for over-current protection.
Why would the factory want to use solder when they are already set up to crimp?
Fit a 1.5A Time-lag (T) axial fuse, get a spare, write the original fuse specs inside the housing, and call it good unless the new fuse doesn't hold.