Forward motion, headfirst & horizontal to gravity!
Haven't done this per se, but from my welding experience came up with these ideas.
1. Use heat lamps to keep the area you are working on from cooling down. Fairly cheap fix, rate of cooling will depend on the ambient temperature surrounding the piece.
2. Heat tape. Found this site(http://www.heatingtapes.com/tape.html). Looks like their mono type tape (for non-conducting surfaces) may work. If you put a dimmer switch on an extension cord you maybe able to regulate the temperature to just below melting (I would check with them first, I have used this type of arrangement to adjust the speed on my hand grinder).
You might try a commercial heat-gun with a "spreader" to redirect the heat from the small round nozzle to a wider area. look at this Snap-on catalog page:
I am sure there are burlier guns out there that can shoot heat even wider than the 3" of the Snap-On.
Hope this helps
That was exactly what I was thinking. I didn't know they made spreaders and was wondering if I'd have to have one fabricated. Thanks.