micro-affair
When you meet someone new and spend a short time with them, whom you share an amazingly strong attraction with, even though it goes nowhere. Craigslist "Missed connections" section is full of folks who had micro-affairs.
I had a micro-affair with the new clerk at Lowe's while she helped me find an item. She's married, I have a girl friend, but we both truly enjoyed each other's company for those brief 5 minutes.