Should be able to find a heat gun for cheap at Autozone or a similar cheap auto parts store. I think I paid $16.99 for mine.
I know you don't want to hear this, but I'd take those splices out and just solder the wires together without them. Makes for a much cleaner install, and it'll also be better in the long run. I've been down this road, and I'm glad I redid everything.
