I don;lt think its a specific brain region. Interpersonal attraction is a rather complex process, and can;t really be regionalized. However, what you're describing a is more simple cognitive process. In lay-men's terms, its called being "turned on."

A psychologist would call it passion[ate love]. Simply the person in question has a body that is sexually attractive to you, maybe some pheromones involved, and quite possibly their personality has some quality that sexually attractive. Typically people only speak of being turned on by someone/thing that is sexualized and that results in an obvious physiological change (such as an erection). However, this isn;t always the case, and you can very much be turned on by a non-sexualized person without the external response.
You ask why evolution made people get turned on even if there's no chance of anything happening. Well, actually, your question is invalid, because you decided that there was no chance after the reaction. The reaction is there to encourage you to walk over and
make something happen.
Also, with the pheromones, it doesn't have to be reciprocal. People don;t really know how they work, and so we can;t say anything about reciprocation. Also, it could simply be that the genes that produce pheromones are complimentary to your receptors without you pheromones being complimentary to his receptors.
Finally, one thing you should understand about evolution, its not logical. Lets assume that the universe is inherently chaotic. out of chaos, there is a possibility that a self sustaining system will come as a result, and produce some apparent logic and procedure. This system here is called life (in another self-sustaining system called our biosphere). Life is a system that has a system acting on it, and so it responds systematically. However, the forces that drive evolution are still a decedent of the chaos out of which life formed, ad are therefore chaotic themselves (are random mutation here or there that either make the organism more or less adaptive to the environment) Over time, the changes seems systematic because the changes that persist are the ones that so happen to maintain the system. Our brains are organized as they are because they
work at the minimum requirement for survival in our environment (and the environment so happened to be one that favored and almost required high degrees of intelligence). They are
not organized because it is the most efficient and effective method of doing things. In the end, my point is;
it doesn't have to make sense.