How to calculate temperature of busbar when current flowing through it is 600A for atleast 10mins?
There is no simple "first principles" formula for this.  You can make a fairly good calculation of power input (I^2*R) but that is only half the equation.  The power dissipated to the environment depends a many factors including the shape and orientation of the bus bar, what it is connected to, how the vents on your enclosure are oriented, and whether or not you have a cooling fan.  

Electrical codes and engineering texts will have "rules of thumb" for different operating conditions.  These are designed to be conservative and safe under most conditions, and therefore do not need to capture the full range of effects.

If those guidelines or other rough estimates aren't good enough you basically have two choices: build the system and measure it or do a simulation with something like COMSOL.