You are right; with the current algorithm it is quite difficult to fully unscramble the image into one single strip. For now, the best you can do is get a bunch (~20) of strips after annealing, and manually flip and rearrange them (in an image editor) to get back the original image.

The default temperature of 4000 is fine for all the example images at 600×400.

The default 30 million iterations leads to a reasonable run time of about 10 seconds, but leaves many small strips after annealing. Bumping up the number of iterations to 300 million, 3000 million, etc. will take proportionally longer time, and give marginally better results.

Based on the description in the webpage, I expected it to work on the default image with default parameters

As stated in the "notes" section, you need to set the number of iterations to about 1 billion, and also adjust the temperature according to the picture's characteristics.