Here are a few thoughts on theory AND practice:
The thermal conductivity of WC (Tungsten Carbide) is about 110 W/mK and for a hardwood is about 0.12-0.14 W/mK. Conversely the heat capacity of WC is 0.28J/gK and for wood about 1.76 J/gK.
This means that the heat generated during cutting will MUCH more rapidly (almost 1000x) flow into the bit than the wood, raising its temperature (remember, heat is NOT temperature). However, when chips are ejected, they carry a fair bit of heat with them since their heat capacity is quite high (due in large part to the water content) compared to the WC (over 6x). If the chips are not ejected but instead reground into finer saw dust, additional heat is generated and little is removed - so the temperature goes up substantially. The result is a scorching of the wood, both newly being cut and the stagnant sawdust. This is where the carbon buildup comes from.
Now the practice - As stated by Chris and Scott, don't baby your router bits. Push them hard enough to create good sized chips, not saw dust. When I first started using a handheld/table router, I rev'ed the speed way up and SLOWWWLLLY fed the work pieces in. Big mistake - a lot of burning. After some experience, I learned to slow the bit down and speed the feed rate up. It comes with experience. The attached picture is a wormy maple table top I routed this weekend with a 1/2" top bearing flush cut bit. Note the good sized chips. and the glass smooth edge.
When I started using my CNC, I made the same mistake - too high of RPM and too slow of feed rates. I guess under the pretense that the more cuts per inch, the better. WAY too much sawdust. WAY too much burnt wood. WAY too much bit wear. With a CNC it's easy to tell the machine how fast to spin and how fast to travel, so, using bit manufacturers chip-load guidelines, it's straightforward.
For a hand-held router, as stated by Scott , I ALMOST always move the router from left to right to keep it from running. The exception is at the left corner of the edge being routed. Start the cut about 1/2" or so from the left corner and route the edge by moving to the right (on the right edge, especially when you're routing end grain, it's often a good idea to clamp a scab on the end to prevent tearout). Then go back to the left side in about 1" and route right to left for that left edge. Keep a firm grip on the router because it will want to run to the left once it hits uncut wood. A scab is not as necessary on this edge, but on a really critical cut, I'll add one. There is a danger of trying to route left to right starting EXACTLY at the left edge - if you are off just a little, you'll dive into the adjoining side and either gouge it or have the router run away from you toward the back of the piece. Since you're not expecting that direction of move, it can rip the router out of your hands and things can get ugly.
Before starting a cut, I always set the router on top surface and get a visual on how much overhang to expect. I also take a practice run down the piece just to get a feel for the total motion involved from start to finish. Then go back to the starting position, set the router on the top surface, make sure the bit is away from the piece and turn it on.
For table mounts, all of the above is the opposite - feed right to left except for the very left edge (yes, left edge). I almost always try to figure out a way to either scab the left edge or rough cut the piece a little long and trim to width later. If the piece is routed on all 4 sides you just have to be extra careful.