Dor,

If the connection has a non-zero resistance, then the potential (with respect to either terminal) changes linearly from one electrode to the other.

Yes, but theoretically speaking, how will it look if there is a zero resistance and all parts of the circuit can absorb infinite amount of heat

Dor,

What is the acceleration of an object of zero mass when I apply a force to it?

If you had a perfect superconductor (ie, one with an infinitely high critical current density) then the limiting current would arise from the internal resistance of the cell. There would be a current in the 'short' but no voltage at its ends - and inside the cell there would be a rising potential difference created by the finite speed with which ions can move to generate the driving current.

May I ask what research you are engaged in that prompts this question?

I'm connecting a solar cell to a battery, or other voltage source.

If the solar cell is thought as a second battery, than it is kind of the same situation. Obviously it is different but I'm not sure what exactly are the differences.

I=Vbat/(Rbat+Rwire) -> Vbat/(0+0)-> infinity

The nature omits any infinity. In case of mathematical model leads to infinity, the mathematical model is wrong (out of applicability). As a rule You needs to take in account second order effects. For example - the wires inductance Lwire:

dI/dt=Vbat/Lwire; Time=Lwire/Rwire -> Lwire/(0+0) -> Time -> infinity

So Yours experiment with shorted battery needs infinity time. Are You ready to wait?

I'm connecting a solar cell to a battery, or other voltage source.

The current is limited by PV short current - ISC. At worst, the current is limitted bu battery fuse.

In case of real nonlinear conditions, You can solve the set of equations:

IPV=Ipv(VPV); Ibat=Ibat(Vbat);

VPV=Vbat; IPV=Ibat;