Router feed rate
When router feed rate is too slow, the wood is ground up into powder and smoke begins to rise. Moving too slowly trying to smooth a cut, your good intentions backfire by increasing friction. While you are pausing or lingering cautiously in a mortise with the bit running, it might be burning.
An inner corner is a likely place for a burn. As the bit enters a corner, its contact with the material increases suddenly. Shavings erupt and have to escape somewhere. In an enclosed spot, a small 2 flute bit does not have much room for conveying swarf. If it cannot keep up, it fills and compacts. Progress slows to a snail's pace. This obstructed situation is a candidate for a flare up. Single flute bits have less contact area and more chip load to win the scooping race. This option is a way of avoiding burns where the bit must be small and feed rate is slow or comes to a halt while running.
Dense, rigid materials are slower to cut than porous ones. MDF takes more time than particle board. Hard maple and oak cut slower than softwood. A motor strains to cut dense hardwood, especially trying to make too deep a pass. If it almost stalls, you may be tempted to compensate by drastically slowing the feed rate. To avoid burning, keep moving and use a lighter touch. After you reach the end or corner, back away slightly.
Variable speed
The other sort of router speed is rotation. If you have variable speed control, you'll notice the speed chart that comes with some big bits. You might see numbers amounting to a precaution, but not a recommendation to improve the quality of finish. A chart can't evaluate the edge or the material hardness, so it can't substitute for making a test cut in a scrap.
The appropriate speed is somewhere below the maximum RPM, so begin a test cut with the variable speed control set to slow rotation and gradually increase until the cut is acceptable. Going full throttle is only for a 1 in. bit or smaller.
To keep it simple, a bit twice as wide should rotate half as fast. At the same RPM or Revolutions Per Minute, a big bit has a faster peripheral surface speed than a small one. If a big bit rotates fast, it burns. To run big router bits slowly, you'll want a strong motor. A shaper rotates slower and has the power for very wide profiles.
Routing Corian
Laminates and solid surface Corian are cut by a carbide bit. The abrasiveness of these materials is an issue. At a slow feed rate the operation can get messy. If it is allowed to warm up, friction burning can melt it. In the wake of a bit spinning too fast, fresh powder sticks to the melting cut and hardens crumbly and bumpy. The scorch mark isn't always dark, so the reason isn't immediately obvious. The mystery is solved if the melting goes away when using a new bit at lower RPM.
Burn marks
A friction burn mark can be made by any place on a bit that isn't a keen edge. A flush trim bit has a round section near its end which can't cut, but mars laminate.
A straight plunge bit cuts on the side, but has no edge on the end, so a burnt chunk is left standing in the middle until you nudge it out sideways.
It is easier to prevent burn marks than to painstakingly scrape them off. At least a knife or scraper gets off superficial burns without so much fuss as sandpaper.
Bit burn out
A bit's small size is a versatile attribute, but it puts a limit on lifespan. Realistically, even in normal use on hardwood or manmade composites, you can use up little bits quickly. Diminutive bits can do a big project, but waste time. Continuous runtime has limits, so you'll probably use extra ones. If there's a choice of a big bit, do not pick up a smaller bit that may burn out early with the project incomplete.
Steel bits wore out so fast that more durable carbide router bits all but replaced them. Routing MDF eats up bits. It generates heat and erodes the tip edges. If you have a fresh spare, do not persevere with a stale, overloaded one that is deflecting and overheating. Burnout is greatly hastened by continuing to use a tired one constantly without pausing.
If the bit is not burning your fingers, all okay. By the time you smell smoke, it has risen a few hundred degrees; that's not so great. If it is blue, that's bad. A bit with a fat stem runs cooler; its hefty mass can help manage the heat.