Start by boiling some water.
While it boils, put the cold hot dogs into your thermos.
Pour the boiling water on top, leaving a little room at the top and give it a minute before screwing on the lid. This will keep the hotdogs hot for up to a few hours.
Grab a ziplock bag for each family member so they can assemble their picnic meal. Add a bun for each hot dog, whatever sides they've chosen, napkins, and their plastic basket. This step is not necessary, but will make assembling each meal easier later.
You shouldn't need individual utensils for this meal, but you might need some for adding condiments. You'll also want to pack tongs to grab the hot dogs out of the thermos. The water might still be pretty hot when you picnic.