Finding the Real \$V_{BE}\$
The 'real' VBE cannot be 'calculated', without making some assumptions, it is what it is at any given temperature and current. The reason we approximate to 700mV, is because that's what it is at room temperature, for a handful of mA, when it's permissible to approximate.

It varies with temperature, about 2mV/C IIRC, and it also varies with current. At low currents it varies according to the diode equation, and at higher currents the residual series resistance of the junction creates an additional drop. I've recently done some measurements of VBE for making a logamp with a transistor, from pA to >100mA, and it varied between 200mV and 900mV.