Say I have a hot dish, and I want to keep it hot and safe (i.e. >140F) without any heat source (no electricity, no fire) for as long as possible, say morning to evening, or even over a day. Just using something insulated won't be enough for more than a few hours, so what else can I do? 
It looks like a popular solution is a good ice chest with heated bricks. I found several variations of this technique on various sites. It's an improvement over simply insulating since you have a lot of additional thermal mass and it's starting out at a much higher temperature.  You wrap the bricks in foil and heat them in the oven (e.g. 30 minutes at 450F) so that they're holding plenty of thermal energy, then line the ice chest with towels to protect it and place the bricks in. You might want another layer of towels around the food too, and you can place additional insulation over the top to fill any remaining space.  Depending on the food, I expect this could actually result in cooking it a bit further, but it'll definitely stay hot a long time. I haven't actually tried this and people's assessments of how long it lasts vary wildly. But given that ice chests can stay cold for a day or two in good conditions, I suspect that if you get the details right, this might well do the same for staying hot. 