I can't answer you exactly as I don't have the facility to hand, but most of our takeoff performance is geared to the weight at which you are getting airborne. You are quite correct in saying that OAT, QNH and field elevation are some of the factors affecting performance, but there are others such as surface condition (wet, slippery, contaminated etc.), engine bleed extraction (are we running the packs off the engines or using anti-icing?) and aircraft C of G.
We tend to enter the performance chart at our take off weight and that will give us the speeds and flex temperature applicable to our weight. These charts are runway specific and include the runway length as one of their factors.
Looking in FCOM 2 at the Quick-Reference charts, just to give you an idea, the figures are given for a 2000ft airfield with a dry runway. You can get airborne with full power at a weight of 60 tonnes at an OAT of +16 on a 1500m runway in still air. Rather shorter that we are all used to, but equivalent to some of the smaller Greek islands. Skiathos springs to mind.
As regards what would be the minimum runway length I would take off from - as long as we have the performance - I'll do it. Don't forget - take off performance isn't just about getting airborne within the length - it's about being able to stop from V1 if it all goes wrong without going off the end!!
I've just re-read this answer and realised it reads like a performance lecture - it's not meant to!!!! But I hope it goes some way to answering your question.
