I'm Dr. Jackie, an interpersonal communication researcher/professor and relationship expert. And I definitely want to help. But I'm not really sure what your question is. Can you clarify? Are you seeking recommendations on what to do next? Or if you should back off? Or what you think is going on with her? If you can specifically narrow down your concern(s), I can better help you. :)
Since you have only known her for 3 weeks, it's a little soon to tell if she is just moving cautiously or if she truly does not want a serious relationship right now. If you say she is "cold on love," what has she told you? At this point, you kind of have to believe what she says because you have no reason not to, yes? So if you really like her, talk to her and tell her you like the gym time and you like going out and you like the physical intimacy. So be honest and tell her you would like to be in a relationship if that is what you want (it seems like it) and see if she is perhaps amenable to it. If she is not and yet she does seem compatible with you, then ask her if something happened that has made her NOT want to be in a relationship.
In short, especially in the beginning stages of a relationship, you don't have a lot of information on the other person in terms of what "makes them tick," or what motivates them. So you have to ask and probe if you want to know.
What do you think about this? I'll also send you my phone and Skype info via the JUST ANSWER form so that you have that if you ever want to use it.
Thanks for following up so quickly. I wish I had the magical answer for you; but the reality is, you have to decide for yourself what you are willing to risk. In other words, think of a see-saw. Everyone just starting in a romantic relationship is on one of these. And on one side is the love and feelings for the other person. On the other side is the vulnerability/risk/fear of getting hurt. And in the behavioral sciences, we actually term this decision/risk or whatever you want to call it as the "Tolerance of Vulnerability." In other words, what is your threshold, or tolerance level? Which side seems to weigh more--your love/feelings for her or your fear of getting hurt? And honestly, it really is like this see-saw where you have to figure out how much "hurt" or possible pain you are willing to risk to try to have a relationship with her. And unfortunately, I can't answer that for you. You have to decide what the risk is worth.
Life is like this in any big decision, including love. If you take the promotion, will the work load be so much that your performance will plummet and you will risk losing your job? If you get a job offer in another state, will you be willing to move away from family and friends? Etc. So unfortunately, I don't have the answer for you--you have to answer that. Many literary figures from centuries ago would say that love is worth it. To paraphrase a common quote, "It is better to have loved and lost, then never to have loved at all" (Alfred Lord Tennyson, C 1800s). Of course, we wonder if that was just poetic or if he had experienced that. :-)
Does that help at least put things into perspective to make a decision? Please let me know.