What about the size of grounding wire? Are they also selected more thicker to increase factor of safety? But, I don't think that will be necessary because the current flows only for very short time.
It's actually more complicated than that.
Protective disconnection devices take finite time to operate. This time depends upon the current. The greater the current the faster the operation.
The UK regulations require the electrician to establish what is known as the 'prospective Earth fault current'. This is a value that operates the design disconnection devices within specified time frames. One factor in this calculation is the 'earth loop resistance'.
The resistance of the earthing has to be such as to sink the prospective fault current within the time allowed in the code.
The code disconnection times vary with location, being shortest at locations of greatest risk.
In theory each location should use the actually measured Earth resistance in this calculation.
In practice a value base on experience is often assumed.
In theory individual earthing cables should be sized according to this process. It is impracticable to size every cable individually so the worst case is often taken and used for the whole wiring scheme or the scheme divided into a few size groups.
These principles also apply to equipotential Earth bonding.
Take a look at this thread for an explanation.
https://www.physicsforums.com/showthread.php?t=520792
Finally here is an extract about transformer earthing from the electricians guide to regualtions.