The ward takes the damage first regardless of what order they apply
The following Q/A establishes that damage to your temporary hit points still counts as you taking damage and with that knowledge, there are two possible cases:
The ward clause applies first; in this case you are no longer taking damage so the temporary hit points won't do anything.
The temporary hit points clause applies first; in this case you are taking damage so the ward's clause will now apply, taking that damage instead.
This is also supported by lead game designer Jeremy Crawford in an unofficial ruling (a tweet):
Q. How do the Abjurer's Arcane Ward and Temporary Hitpoints interact? Do they stack? If so, which is depleted first?
A. An abjurer's Arcane Ward takes damage first. Any leftover damage is taken by temporary hp, then normal hp.
It's different if you believe temporary hit points taking damage doesn't count as you taking damage
However, you could also say that damage to your temporary hit points does not count as taking damage (asThis stance is taken by the second answer to the initially linked question does). Inand in this case, the order will matter because either clause applying will result in you no longer taking damage.
In this case I would default to the optional rule from Xanathar's Guide to Everything for resolving simultaneous effects:
In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen.
Either way, you never make a concentration check
Note that under either belief, no matter what, a concentration check will not be made. In the first account the ward is always taking the damage, not you; in the second account either the ward of the temporary hit points take the damage and neither would count as you taking damage.