Is there anything special about the extension? Is it just a piece of machinery steel like C1045 for example?
I'm not much of a fan of pinning extensions onto shafts. We weld 'em on solid right through to the center. We simply use an oversize piece for the extension, weld it on reasonably straight, and then 'machine it straight' after welding is all completed. I never arc weld in my good lathe
But I do have various crude V blocks and stuff back in the welding room to position stuff like two shafts for a butt weld.
A simple V shaped (or U shaped if it is a large shaft) wedge prep on the end of each part is the preliminary step. This can be ground on pretty quick, cause nothing is hard to a grinding wheel
I would fill in the center hole with weld at some point during this prep step.
Now, granted, the arc weld is going to draw out the temper a little too far on the hardened piece. You want it to, because you don't want the weld zone to be brittle hard. A small shaft like that will overheat pretty quickly with normal arc welding procedures, so I would not preheat it. But still, I would watch the amount of heat input to try to keep the colors from going too far up the hard shaft.
I'm more familiar with stick and MIG welding and I would stick weld this with 7018 x 3/32. It causes a bit more heat input than the MIG, but the MIG is almost too fast, and the quench effect of the cold parts is significant. Stick, because is it slower, will put a little more heat into the joint right on the initial passes, which is what you want to get a tempered weld zone. After the first couple of beads (on opposite sides of the V prep) you can begin to watch the heat buildup, and cool it with an air blast, not right down to cold, but enough to keep the high heat from travelling too far away from the weld area up the hard shaft.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)