Apologies for not reading your question in sufficient detail.
Cutting speed is definitely your problem!
Routers rotate at speeds 10 times higher than drills! The no-load speed of a router is typically in the range 8,000 to 25,000 rpm whereas a drill will only run at perhaps 2,500 rpm.
You have to remember as well that it is velocity at the tip of the cutter which counts - not just the rotational speed. The larger the diameter of the cutter at a given rotational speed, the higher the linear velocity at the tip - and that's where the burning happens.
I dug out an old router bit catalogue (Trend actually!) and they recommend that for hinge sinking cutters over 25 mm in diameter, that you run it in th erange 2,000 -12,000 rpm to avoid burning. It also recommends: USE WITH PILLAR DRILLS ONLY - which is what I suggested before!
Good luck and don't forget to wear your goggles!!!!
JD, March 2008