Hey Peter,
I agree with the other posting on getting a different power carving tool. I carve for a living, have for 15 years. I'm also a tool freak..so when I saw a big dremel machine with a pretty high RPM rating comparatively.....I jumped on it.
I had the exact same problem with the shaft/handpiece heating up.......I tried replacement, overlubing the cable, pretty much everything you can do, with no luck.
The cables suck badly, the lil attachment dog where the handpiece clicks on aren't big enuff, and under torque the spin in the slot of the handpiece........ripping the crap out of the handpiece. Mine succeeded in chewing up 4 handpieces.
I ended up replacing the dremel with a Mastercarver unit from Woodcarvers Supply, after being left stranded numerous times in the middle of some fairly high dollar custom carvings in moose antler. This unit is a lil more expensive........but runs at the higher RPM, and also has a reverse on it.
Ive used this tool for the last 5 years, with absolutely no problems, except for maintainance. I have an older foredom as a back up unit.I also have a light duty dremel flex shaft Ive had for 10 years that is still working like brand new(I keep a small detail burr in it I use pretty frequently.)
Dump the dremel, and get yourself a decent carving tool.......you will be doing yourself a huge favor, and be $$$$ ahead in the long run. That large flex shaft was dremels foray into the world of big boy tools, and it failed miserably.......you said it wasn't being manufactured anymore.......ya reckon theres a reason for that??
Steve @ Creations by Black Hawk Custom carvings in Antler, Bone,and Stone