Say that you've go 10 temp hp and are maintaining concentration on a spell. Some punk goblin hits you with an arrow for 5 hp damage.
Do you have to make a concentration check? You haven't lost any "real" HP...
My instinctive response was "yes, you have to roll," but when I went to look up the rules, I found it was not as clear-cut as I originally thought. Here are the concentration rules:
Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon's breath, you make a separate saving throw for each source of damage.
And the temporary hit points rules:
When you have temporary hit points and take damage, the temporary hit points are lost first, and any leftover damage carries over to your normal hit points. For example, if you have 5 temporary hit points and take 7 damage, you lose the temporary hit points and then take 2 damage.
Note the phrasing of the final sentence: "If you have 5 temporary hit points and take 7 damage... then
take 2 damage." The way this is phrased suggests that the temporary hit points are intervening before the damage actually hits: "Take 7 damage" is replaced with "lose the temporary hit points and take 2 damage." So "take 4 damage" would be replaced with "lose 4 temporary hit points and take no damage," which would mean no Concentration save.
Purely based on the text of the temporary hit point rules, this is the logical reading. However, this has somewhat far-reaching implications. It means that any time a PC with temporary hit points gets hit by something with a rider effect (e.g., poison), you have to consider whether preventing the damage should prevent the rider effect as well.
It also makes temporary hit points far more valuable to spellcasters.
Armor of Agathys, for example, would be a must-have spell for bladelocks. That isn't necessarily a bad thing--bladelocks kinda need the help--but it's something to be aware of.
Ultimately, I think I would go with my original response, but that is my personal ruling, based less on the RAW than on a sense of "do not open a can of worms if you don't have to."
(If you put stock in Sage Advice,
Jeremy Crawford says you have to make the save. However, he does not justify this with any citations from the rules.)