Do multiple sources of temporary hit points combine, or do you only get one set?

Question

Do multiple sources of temporary hit points combine, or do you only get one set?

For example, say you cast armor of Agathys and false life on yourself. Do you have two separate pools of temporary hit points, or do you have to pick one of the two? By separate pools, I mean that you have 5 temp HP from AoA and 8 temp HP from FL. If you take 10 damage, can you pick one of the two pools of temp HP and take the leftover damage to your real HP, but still have the other pool to protect against a second attack?

I ask because a warlock player in my game insists that she gets both pools, but I think it should be either-or.

How do multiple sources of temp HP interact with one another?

Answer 1

This is answered on page 198 of the PHB under the section titled Temporary Hit Points:

If you have temporary hit points and receive more of them, you decide whether to keep the ones you have or to gain the new ones. For example, if a spell grants you 12 temporary hit points when you already have 10, you can have 12 or 10, not 22.

Meaning that you choose which source to keep when you gain the temp HP and the other lot disappears. You don't have two separate pools and they don't stack so you either have the temp HP you gained from False Life or the temp HP gained from Armour of Agathys, not both.