Heating one spot in glass until it starts to melt will create stresses,
which your instructions may remove. I used to do some scientific glass
blowing with Pyrex and everything made went into an annealing oven,
which does just what you said. When using the pieces an end would be
cracked off a cylindrical piece and the crack could be fused back
together leaving uniform stresses around the cylinder.
Pyrex used to be a particular borosilicate glass. Pyrex is a brand name,
and the owner now uses the name for a different kind of glass, not as
low expansion.
Use something like silicon carbide paper to smooth a sharp edge.