Copper has a thermal time constant of 9,600 seconds for a cubic meter. For 0.1meter, ThermalTC is 100X faster. For 0.01 meter, ThermalTC is another 100X faster, thus 0.96 seconds. With 1cm being a sizable bussbar thickness, we now know the BB will temperature-stabilize within some few seconds.
The volume of the bussbar is needed, so you know the heat-storage ability of the copper.
You already have the other equations.
Assume one milliohm resistance, at 600 amps. That is 3,600 watts.
In 1 meter long bussbar of width 10cm and thickness 1cm, I'd expect one degree per second temperature rise.