What causes the print heat to 'catch' on the part?
I think that you should first verify that you have the latest firmware and a newer version of MakerWare. I experienced similar issues around that version of MakerWare and remember a lot of print errors came with it.

I believe the MakerBot Dual firmware is somewhere around 7.? and is no longer in development.

MakerWare is also no longer in development as a standalone application and seems to have been ported over to the MakerBot Desktop. However I've personally found v2.4.1 to be substantially more stable than v2.2.

I have not tested it, but supposedly the new MakerBot Desktop (v3.10) is compatible with the Replicator Dual "Original". I had tried an earlier version of MakerBot Desktop and reverted back to MakerWare 2.4 because I ran into issues with connectivity. However, I'm not certain it was an issue with software so much as the exploding voltage regulator...

It might be best to give the new software a shot and/or try v2.4 of MakerWare, if you can find it.

Here's the link to the latest MakerBot Desktop

Here's the release notes for MakerWare/MakerBot Desktop v1.0-latest (v3.10+)