Epoxy will harden up to the point of being extremely hard to sand smooth if your not using a grinding disk
but it'll make one strong bond.
I think your onto something with the heating though - plastic cement (The clear stuff that smells like alcohol that people use to assemble plastic models).
It essentially is plastic's equivalent to welding as it melts the plastic that it comes in contact with allowing you to clamp the two sides of the crack together so that they can fuse while drying. The process is purely chemical so the heat generated will definitely not be enough to warp the plastic.
"Games Workshop" has a really good one for putting together the warhammer type armies.
Hope that helped!
Cheers!