Me and my partner live far apart from each other and it is not possible at the moment to see each other and satisfy our physical needs. So we have conversations that include intimate and arousing talk to make up for that. However, after talking for a while it may lead to one of us having an orgasm from the speech and being aroused for so long

Would it be permissible to continue such conversations knowing it will cause an orgasm from the prolonged arousal? Or with the intention to orgasm through this way (not touching oneself)

As long as the person you are talking is halal upon you there is no problem with having that conversation and no problem with arousal without touching oneself.