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Most drill bits are made from high speed steel, they can get quite hot and not have a problem, not quite red hot.

Very easy by hand with a reg pedestal grinder, at least for bits larger than 1/8 or so, smaller can be done but really good eye site req. The point the bit can be smaller angle 60 deg for soft metals, and flatter 118 deg for general metals, for grinding all you are doing other then producing an edge is to relieve the metal behind the edge, too flat and you get more friction, too relieved and the edge is weak. Try to keep the cutting surface lengths the same length, unless you need the bit to cut oversize then you can make one longer, just rest the bit on your finger near the wheel, bit cutting edge facing up and horizontal gently push into the wheel while moving the back of the drill bit down with your other hand, start with a 1/4 to 3/8 bit so you can see what you have created.

For soft materials and plastics you can grind the face of the drill bit flat or negative angle, keeps the bit from corkscrewing into the material.