... or Campfire? Kidding aside, we'd need to know what you intend to solder. That picture is really small, but if the problem is "The thing doesn't work, and I can see a break in the wire," then soldering the gap would likely return it to a functional state. If instead the question is "Can I run a solder line across the entire thing," then sure, but the odds of it giving birds a pleasantly toasty spa experience go way down because you'll have shorted out the heating element.