You know how it's generally accepted fanon that Nine's regeneration into Ten was at least partly influenced by Rose? He turned into someone younger, more conventionally attractive, he took her accent, had Christmas dinner with her family etc. etc.
So taking that one step further...
The last thing that the Doctor experienced before retenerating in The Stolen Earth was that crazy JOY at seeing Rose again. He ran towards her like a total dork and then basically went and died in her arms. Ten II was then created out of that regeneration energy (with a little help from Donna and the Doctor's Hand - and, WOW, this show is on CRACK).
One of the things that separates Ten I and Ten II? Ten II's ease at opening up to Rose - asking her to spend her life with him, and then telling her he loves her. We don't know exactly why Ten I couldn't say "I love you" - possibly because he wanted to make things easier on Rose, possibly because he couldn't handle opening himself up for that much hurt. I think Julie Gardner suggests in the Confidential that it's the human part of Ten II that allows him to say "I love you," but I don't really like the implication that the Doctor being an alien or a Time Lord somehow makes him incapable of love. Because I think we've seen time and time again that the Doctor can and does feel things as deeply as humans.
But what if Ten II was influenced by what Ten was feeling when he began to regenerate? Which was probably some combination of: "OMGSQUEEROSEISBACKMUSTCLINGFOREVERWOOO" and "OH CRAP, I GOT SHOT BY A DALEK." Which would help explain why he's eager to spend his human life with Rose, and why he's able to open himself up to loving her fully. It's like Nine's regeneration into Ten gone haywire. He didn't just regenerate into a romantic partner for Rose - he's also got one heart and can age at the same time as her.
Okay, this is kind of whacky, I know, but at least it helps me get some sense of how Ten II was feeling with regards to Rose, especially since we didn't even get to see them interact until the Beach Scene Redux. *eyes RTD*