The fact that you can lift the door to get it to latch tells me that it is likely the installer did not install long screws through the top hinge into the 2" x 4" or 2" x 6" that creates your opening ... read more
I would recommend not less than 40 degrees. If the shingles are a dark color in direct sunlight they will seal in one day from the solar radiance from the sun even if temps are low.