To write a thesis statement for a correlation between Hewett's childhood and "The White Heron," it is best by comparing the two. If I were writing the piece, I expect that I would compare Sarah as a child to the white heron.
The white heron is described as being a rare bird: uncommon and hard to find, unlike the other birds that Sylvie, the main character, knows so much about. Sylvie knows of the bird and has probably never thought to hurt it or any of the birds of the forest that she loves, but learns that this is the intent of the young man who visits the farm. He wants to kill the bird, stuff it and put it in his home.
In comparison, Jewett is described as being an unusual child for her time. When most young women were be taught to sing, dance and do needlework, preparing to be wives, the Jewett daughters were educated. In being taught how to read, Jewett developed a love of writing. She was also unusual in that she wanted to study to be a doctor like her father, something also unusual for a young woman in the 19th century. (She was unable to do so because of poor health.)
If I were to write a thesis statement to prepare for an essay discussing this comparison of the unusual white bird and the unusual young woman, it would probably state that one might see how Jewett would identify with the rare white bird, which was not like the others in the forest because Jewett herself was also rare and unusual in the society of which she was a part. Her character’s desire to protect the white heron might parallel her desire to hold on to the wonderful days of her youth, especially the time with her father that was so dear to her.