<human>: Can you provide a brief rundown of the text in within 3 sentences?

Quick background on the topic, I have been living with my roommate (let's call him Jack) for close to 3 years now so we have developed a really strong friendship. I just got out of a pretty serious relationship of 2 years about a month ago and the Lady in question (let's call her Jill) has been divorced for a year.

Jill is from out of town, on summer vacation, has been staying at our place and at her parents house, leaving end of august. We met briefly a few years ago when she was engaged and got along well, but nothing romantic by any means. Now here is where it gets tricky...

Jack works out of town for two weeks at a time, so this past week it has just been Jill and I at the house and we have really hit it off. Tons of shared interests, telling jokes, having serious, playful, and intellectual conversations (something I missed dearly in my last relationship)...we stayed up until 4 am just talking the other night, it felt like time was standing still we had so much fun together.

Since that night, we have both been a bit more flirtatious, more 'curious' eye contact, sitting closer to each other, etc. So I am not convinced that I am just chasing my tail and that she has started to take a liking to me. Now I am 100% certain that Jack would NOT approve of us seeing each other in any way, so I am leaning towards not going any further than this current flirting stage out of respect for Jack, but at the same time I believe it will be pretty difficult to do so when I am going to be living with a woman that I find very attractive on a physical and emotional level for pretty much a whole month.  How should I handle this situation /r/relationships? I would turn to my friends for advice but Jack and I share quite a few mutual friends and would not want news of this circling back his way.
<bot>: Living with roommates sister for a month, both of us have startedshowing signs that we are interested in each other, don't want to damage relationship with roommate.