dnd 5th – Is a concentration check necessary when temporary hit points absorb all damage?

Yes (probably).

According to the designer and official rule expert of the 5th, Jeremy Crawford, "When temporary hit points take damage for you, you still suffer them, but not your actual hit points."

On August 25, 2014, Crawford was questioned about a similar situation that occurred twitter by @Mathew_Reuther:

@JeremyECrawford If my temporary contact points are 10 and I suffer 30 damage from an attack, what is the control center of my concentration check?

Crawford replied:

@Mathew_Reuther The CD equals 15. When temporary hit points absorb damage, you still take damage, but not your true life points.

For a concentration control, "DC equals 10 times the half of the damage you suffer, regardless of the highest number", so, in the Twitter example above, DC 15 is based on 30 damage. (PBR, p.80, PHB, p.203) Although this situation is not entirely relevant, the character having suffered real damage over the temporary PV, Crawford's statement seems quite clear.you still suffer damagebut not at your true reach. "

however, if the real the damage was totally reduced (not absorbed), so there would be no control of the concentration. See, for example, the Monk Deflect Missile function, the Parry Combat Maneuver and the Heavy Armor Master feat. (PHB, pp. 74, 78 and 167)

Also, Arcane Ward's function to abjure it has its own health points1 and[w]when you take damage, the ward takes the damage instead."(PHB, p.115) Thus, an attack fully absorbed by the guardian is not a damage taken by the character and no verification of the concentration is necessary. (Courtesy of @Dungarth)

  1. Instead of giving a character temporary hit points like some magic spells and items.