I'm interested as to why many posters have concentrated on the fact that OP didn't "do" anything, when the really interesting thing is that she did. Mrs C., - it sounds as though you have had a huge emotional response to the man - to the extent you've experienced it as a physical event (body shaking etc) - that most certainly is something!
My take would be that there are certain times when we "open to approach" iyswim.. lots of single people aren't (I wasn't for a long time)... but it sounds like your marriage being less than you want has made you receptive.
Was he playing you? I doubt it tbh. Of course, many man will feed you some lines and a pina colada and chance their arm - but what you describe is an intense phsyical reaction, and I think it is difficult to orchestrate that.
It does sound like you had some sort of intense connection... I disagree that it would necessarily wear off once the initial excitement is passed... but if you belive the romance of it all, and that he is "the one" or whatever, where does that leave you.
What to do? See him again, and you will swirl in deeper. Affairs are miserable and depressing. And the worst possible way to end a marriage...
Though it probably feels exciting and interesting to turn this strangely exciting meeting over and over in the safety of your own mind or MN today, this chance encounter is not a good thing... unless you;re thinking of throwing your lot in with the stranger and ruunning for the hills....
Do let us know what you decide!