No. According to media reports, the woman in the picture has stated that the photo was staged, and intended to be a joke:
If the story is too good to be true, it's because it is. Roberta says while she shared photos of herself baking bread in the mailbox, it was all in fun.
"I believe some people believe that," Wright explained. "It's not exactly what happened. It's the storytelling of your imagination." (ABC13 Houston)
It seems, though, that the bread was indeed in the mailbox for at least some time during the preparation process:
"So technically, I proofed it in the mailbox and then I finished baking it inside," she said. "My daughter was telling me to be careful how I was saying this because I didn't technically bake it inside a mailbox, but I just loved the illusion."
The term "proofing" in breadmaking refers to the point at which you allow yeast to ferment the dough, causing it to rise. Once risen, a baker then pops it in the oven. There's a big range of temperatures for proofing bread, from 50 degrees Fahrenheit all the way to 110. (chron.com)
So while the temperature inside of the mailbox may be high enough for proofing bread, it's certainly not high enough to actually bake it.
Also note that the media reports usually don't fail to mention that the woman in the picture has recently published a children's book that seems to play with the topos of the quirky grandmother, so the whole story is very much on-brand. One thing that we can be sure is that the picture going viral will not hurt the sales of said book.