Ok, so I know this is kind of morbid, but it’s more of a question about the nervous system than it is really about boiling someone alive.
As I understand it the nervous system is designed to respond to changes in the environment.
Say you put the heat up on boiling water extremely gradually. Would it be possible to boil someone without causing them pain, or will at a certain temp the body just naturally respond to it?
That doesn’t even work with frogs, let alone humans.
Have you never been in a Sauna or hot whirlpool?
Try the following self-experiment: sit in a half-filled tub with comfortable warm water. Turn the hot water on and see how long you can bear it. There will be a point when it’s too hot, before you’re really burning (though your skin is very red).
Ah, I imagine that your victim would croak before the water got to the actual scalding phase. When immersed in hot water, your body can’t use the usual temperature regulation processes. It looks like a hot tub temperature of 106-110 degrees is enough to possibly cause heat stroke and unconsciousness followed by subsequent drowning. So once you get into the 110+ territory, your victim will probably be uncomfortable but not in unbearable pain up until they pass out.
There’s changes to an environment, and then there’s changes to the environment 
Yes, you probably react worse when you go from an 80 degree room to a 30 degree outside compared to gradually cooling the 80 degree room to 35 and then going outside
but exposing a human body to ranges beyond what is found in our environment? there’s no evolutionary mechanism that would necessitate it, so the ability for the nervous system to react would probably be non-existent.
As was noted, if you do it slowly enough to expect habituation, the victim will probably die of hyperthermia before serious skin damage takes place. From what little I know of physiology though, I think habituation doesn’t work for pain stimuli the way it does for things like smell or hearing, and this is in fact why chronic pain is such a very serious problem for some people: you don’t get used to it, it just hurts all the time.
OTOH, if you do it really fast - like this guy - you kill off all the nerves in the skin, and you probably won’t feel much before you die.
I think what the OP is really trying to ask is how the nervous system experiences pain. Is it the large differences (i.e. going from normal to extreme in a moment) or is there some threshold beyond which the pain receptors will be activated. A better question might be what would happen if I brought a hot poker ever closer to your face over a long period of time (assuming the poker maintains temp). Eventually you are going to feel the heat and could probably ignore it. But, is there a definite moment when the body will say “Whoa…too close”?
You are correct that the human body senses changes in temperature rather than absolute temperature. An interesting experiment is to put one hand in a pot of hot water and one in a pot of cold water and let them get acclimated to it. Then run your hand under medium temperature water, and one hand will feel hot and the other cool.
You also happen to have two different heat related pain detectors in your skin. The first one kicks on at about 45 deg C, which is hot, but not actually to the point of causing damage to your skin, and the second one kicks on at about 51 deg C, where damage actually occurs. These are called your VR1 and VR2 pain receptors. The VR1 pain receptor also happens to respond to capsaicin, which is the chemical in hot peppers that makes them “hot”. Birds (and some other animals) don’t happen to have the VR1 receptor, and therefore can eat hot peppers without feeling “hot” from them.
Since the VR1 and VR2 pain receptors turn on at fixed temperatures, you’re not going to fake them out no matter how slowly you raise the temperature.