Wow, that's a tough situation. My first thought is......who would leave for days and leave a heat lamp on? I'd be afraid of a fire. You can certainly tell them it isn't safe to leave a heat lamp unattended. They could start a fire that burns down your house. Beside the fact they're burning the chickens, that's just idiotic! As far as neglecting the chickens go....not everyone keeps their chickens in totally sanitary conditions. Not everyone free feeds as much as they will eat. I clean my coop, fill food and give clean water daily. Not everyone does so I think you'll be treading on thin ice on that note. They'll probably give you some excuse that their sitter forgot or had some reason why he couldn't make it.
It could be that these people had good intentions, and were depending on someone to care for them well while they were gone. It may not be their fault that the person never showed up. I would just let them know that you became worried, not seeing anyone come to check on them, and what you found. I wouldn't be accusatory because they may have trusted the person to care for them. Some people don't realize how dangerous heat lamps are, and also don't realize that chicken won't move away from them, burning them selves. Lamps should alway be 18-24 inches overhead, and should never be left unattended. You have to live near these people, so you may want to give them the benefit of the doubt. It's just too bad the chickens suffered, and were burned.
Well first I want to say good for you going over there. Second ignorant is fixable, they may simply not know anything. Or as you surmise don't care but there is one sure fire way to find out. Talk to your neighbor over the fence, gauge their knowledge and involvement. If they are ignorant offer to help. If their simply dullards who don't care you can go several ways. Report them to the authorities if you live up north, offer to take the chickens "off their hands" either for free or a nominal reimbursement. Or gorilla chicken keep like you have been. I know how you feel our, neighbors keep animals all the time but they rarely care for them well. They let their chickens free range as well as their goat, but they do so in our vegetable patch and yard. We have noticed this only happens when they are short on money (or so it seems). I personally feel if you can't don't but if you must, ask for help. To avoid the garden raids we are installing fencing around the veg garden. Also I have been supplementing the feed forage available to the neighbors animals At first my wife and my neighbor where irritated with me but I don't care. Like I told both of them the animals haven't done anything but be animals. And if we can or want to feed them a bit extra that's our prerogative. So for us it has worked out as a happy medium. Best of luck to you and hope it works out well.
That's a tough one. My neighbors are almost clueless. First they didn't know that they had 5 roosters in their flock. They don't worm or dust. They have hatched chicks in the coop from eggs that were hidden. However, they built their coop under a shade tree, it has good ventilation. They cover the openings with blankets when it's cold. They give them gobs of layer pellets. And the chickens get a big tray of leftovers every day. It's tough to see what I could help them with, but they don't speak English . I hope you can figure out how to tell them some things that they will take care of. But there's only so much one can do.