No, Iss would only change if you had a point-contact diode, or some other odd geometry, and the depletion region varied; for a planar transistor, it's a device constant. Vt, of course, is proportional to Kelvin temperature.
Define 'close proximity'; on the same die? If things nearby are dissipating power, they make temperature gradients.
So, use a quad transistor, and use one for logarithm, one for thermometer, and two for heaters.