I used to design torture equipment (er, I mean test equipment) for a neurobiologist who was studying pain. A lot of our tests involved heat and cold. I can tell you from experience that the human body does some weird things with respect to heat and cold. For instance, it has a hard time determining absolute temperature, but a much easier time determining relative temperature, so you can in fact make minor temperature changes slowly and people often won’t notice. You can take a temperature probe and put it on someone’s skin, and if you slowly raise the temperature, they’ll tell you that it is staying the same. Then you suddenly cool it down to its original temperature and they’ll tell you it dropped to being colder than what it started as.
In some respects this legend is based on some real effects that happen in the human body, but it only works so far. I found that if I slowly increased the temperature, my heat pain threshold went from about 44 to about 47 deg C, but now matter how slowly I increased the temperature, once it got about about 47, it f-ing hurt. The “ok enough” temperature varies a bit from person to person, but it’s usually somewhere between 42 and 46 deg C. If you play around with heat torture devices all day long you get a little immune to them, and researchers who work on this stuff usually have a pain tolerance closer to about 45 to 48 deg C.
There’s no way in heck you are going to get the temperature above 50 deg C without someone screaming in pain, no matter how slowly you raise the temperatuire. But as others have pointed out, you can die of overheating long before you literally get boiled to death.