I haven't done it at Disney- but I have boiled hotdogs at home, and heated baked beans hot on the stove, then put dogs in thermos lengthwise,fill with beans- like 5 hours later they're still piping hot for lunch while out somewhere(like skiing) I just brought along paper plates and forks....
For cold picnics, I used to boil the dogs,then cool them down fast, slice them and toss them into a tupperware box, in another tupperware I'd add small cubes of cheddar cheese- bring ketchup in a 3rd container-keep in iced cooler- when it's lunchtime, the kids enjoyed eating their lunch with a toothpick (like at a party) add crackers or some fruit and drinks- lunch-portable and inexpensive!
(I personally cook the 'dogs' before eating, but you don;'t have to)
at first my friends were horrified until I pointed out that bologna and many lunchmeats are just larger versions of those hotdogs

And then their kids would ignore the deli food,and eat our stuff......

It's amazing how tiny that box of food looked in the cooler,but we always had enough to share.....
At WDW,when we had a stroller, we packed salami and provolone sandwiches (they pack well,and don't spoil easily) along with drinks in a small lunchbox- then get snacks later as we liked.....
Now we just split a CS meal, MORE than enough food for 2 people! (2 meals,1 lg. soda feeds 4 people)