The temperature at which "sugar" burns, i.e., goes from sweet caramel to bitter $%@! is called the "scorch point."
Scorch temperatures can be a bit misleading in that thermal transference properties of radiant, contact and convection heat are very different. What will scorch in a pan (contact), may not in a broiler (radiant). What may scorch under a salamander (radiant), may not in an oven (convection). As you probably already inferred the hierarchy from most to least efficient is contact, radiant, convection.
Another variable is the heat transference properties of whatever substrate supports the rub (or sugar). Generally the more like a liquid (custard for instance) the better the coefficient of heat transference, and the less likely you are to burn. Of course, the substrate's temperature is important too. For instance, it's easier to "brulee" sugar without scorching on top of a cool custard than it is to make brulee strings in a room temp aluminum pan.
Also sugars in solution as opposed to sugars as granulates are very different beasts. In food prep, it's damn near impossible to burn solute sugar because the evaporation of most (food) solvents keeps the overall temperature of the solution below the scorch point -- which itself is raised because solute sugars have a higher scorch point. When a water/sugar solution goes over 320 deg F, there is no more water. Even though a clear solution, it's 100% sugar and the color change is rapid. Burnt happens at around 350 F.
In a rub application it takes a long time for the rub itself to hit burn temperature in an oven or smoker at 350 because the substrate absorbs so much of the heat energy, as well as supplying moisture to the rub. Nevertheless it's a good idea not to exceed a 325 cook temp if your rub has much sugar in it.
At any rate the process in which sugar goes from sweet to carmel to burnt is called caramelisation and involves the chemical transformation of sugar molecules into a class of chemicals called furfuryls. Sucrose and fructose sugar molecules (sort of) contain water molecules. The furfuryls start to develop as the water is lost. This may be what Sapo meant (?). This is also why I said dissolved sugar has an elevated scorch point.
Caramelisation is analgous to the Maillard reaction and Strecker degradation, the processes by which meats and vegetables brown. Both require amino acids, and the Strecker degradation a special class of chemicals called carbonyls. Barbecue people don't talk much about the Strecker, but the Maillard reaction gets bandied about now and then because of it's association with meat. (8 times out of 10 when someone uses the term "Maillard reaction," he's a colosshole trying to impress.)
As a general rule the more "brown" a sugar has in it, the lower the burn temp. The brown is a sign of molasses which has either been left in the partially refined sugar (as in turbinado or piloncillo) or added to white sugar (as in regular brown sugar). FWIW, turbinado is partially processed raw sugar with only the surface molasses removed. Gur, jaggery and piloncillo are different names for entirely unrefined raw sugar. I thought turbinado caramelised at a lower temperature than white, but apparently was mistaken.
I know there are sugar burn temperature tables on the internet, but I can't find one.
Confused? Me too.
Hope this was more fun than overload,
Rich