Are you sure he had his heart broken?...seems if that was the case he wouldn't already be wanting to meet someone new. Maybe he was more disappointed things didn't work out but not to the extent of being heart-broken.
Aside from that if you are not comfortable meeting in person yet, just tell him you'd rather talk a bit more before going out. Or if you would potentially like to meet him but you don't want to jump into a relationship, you could express willingness to meet but just be clear its to get to know him and your not agreeing to be his girlfriend yet.
I don't think its super weird he's interested in you so soon after his break up, my boyfriend met me shortly after ending things with his ex and things have worked out great between us.
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Tis the time to melt the Ice.