Its been along time but I'm familiar with that process. Basically the wood will expand the warmer it gets therefore it can absorb more stain, in theory. warm stain will also penetrate better, in theory. Try warming the wood real well along with the stain then soak it over night and see how much more stain it will absorb. Id use scraps to play with. The diferance may not be worth the effort to you. I know cabinet guys who will not stain wood in an unheted area because they say it doesnt take the stain as well.
There are many dyes out there aswell.