Per the M56 tech tips pdf in the link above: "Hold the engine at a 45 degree angle, filling it with oil to the bottom side of the fill and drain opening. By doing this, the gearbox will be filled with approximately 80 cc's of oil. Use motor oil SAE 50 or gearbox oil SAE 80. After the break-in period of 500 miles, the oil should be drained, refilled with fresh oil, and then should never require another change."
I haven't ever cracked an M56 open yet, but I don't imagine you should have to heat it to do so. Probably need to for removing the old bearings and possibly installing the new ones. Again, haven't taken this motor apart so I can't even visually think of what it looks like inside.
Gears are probably fine. Hard to say for sure though without looking at them.