Under what circumstances is it appropriate and inappropriate to act on an initial short-term attraction toward someone?
So many words in this question have a breadth of meaning which make a difference in how it could be answered. For example, certainly not everyone has the same definition of "appropriate" and "inappropriate." "Act" can certainly have a range of meanings, but "short-term" is the most curious word. Does this mean the attraction is short-term or the potential relationship stemming from the attraction is short-term? In any case, it is always best to remember that not every feeling or impulse must be acted on.
There are several certainties for a person who is wondering about this. First, people who are already in a committed relationship should never act on any kind of attraction to someone else. Second, if the object of the attraction is already in a committed relationship, no person should take any action to tempt him or her. These two things are inviolable rules for people in committed relationships.
If both people are "free," which may or may not be a knowable fact when two people first meet, certainly there is freedom to act appropriately if it is in an appropriate place in an appropriate environment. If one of the persons is drunk or otherwise impaired, for example, no amorous action should be taken; the same is true if both of them are impaired. An office party, for example, is also probably not the proper environment to express such an attraction.
These things are all considerations; however, following the norms of decency, honor, and propriety when meeting anyone--especially someone to whom you are attracted--is likely to yield the most productive and happy relationships.