if you are trying to smash it at some point, avoid the whole "your hot" deal. if she really is hot, she's used to hearing it all the time and you aren't distinguishing yourself from the rest of the crowd.
3k miles away and someone you rarely speak to? gotta say it's a bit awkward.. cause what do you expect her to say in return? thanks? i'm guessing she's not going to know how to respond.