Question When sizing conductors, should I use the temperature limit of the connection (which is smaller) or that of the ground conductors?
Answer It is unlikely that the current flowing through the connection will be a source of problem, given that it has a larger cross section available for the flow of current. At any rate, the maximum current that can flow through the connection without damaging it is independent of the size of the ground (and lead) conductors.
The temperature limit of the connector could affect the sizing requirements for the ground and lead conductors because of heat conduction from those conductors to the connector. This could lead to a rapid rise of the connector's temperature to about same level as that of the lead and ground conductors to which it is connected.
You should check with the manufacturer to find out what the current limit for the connector is, and also inquire about its behavior as a "heat sink". If the manufacturer cannot provide you with enough information to make an informed decision, then we would suggest to err on the side of safety and size the ground and lead conductors based on the stricter thermal requirements of the connector.
Note, however, that the current will quickly dissipate in the grounding grid: a few grid meshes away from the connection point, the current circulating in the grid will be much smaller, and smaller conductors could be used. This may not be very useful in practice, however, if several pieces of equipment are connected to the grid. Also, you could reduce the size of the ground conductors by installing two connections (sufficiently far apart) instead of one for every piece of equipment.