I spent the day talking to Echo Factory. Here is what they told me about this problem.
This condition is commonly called trimmer line "welding" and results from ultrasonic resonance of the line within the spool. It can happen with any type of line, but is more prevalent with round shaped line than with square or hexagonal line. The ambient outside temperature does not significantly contribute to line welding. Line welding is encouraged by: sustained high speed trimming against a hard stationary surface (fences, curbing, walls, etc.) and wrapping the line on the bump head spool in a rotationally twisted manner. You can minimize line welding by using a lower head speed when trimming against hard objects and varying the throttle speed. It also helps to let the line hang free and rotate the spool around the line when loading the spool. Most people hold the spool stationary and wind the line around the spool. This technique tends twist the line rotationally which causes the line to bind and fuse together due to the ultrasonic vibration.
To avoid this problem, he told me to soak the trimmer cord in water 24 hours or more before using it, as it will make the cord less brittle and more flexible. Also to spray lube on the cord. If the problem continues, to use a cord with aluminum or titanium in it.