I'm thinking of going a bruiser warlock, original I know, with some barbarian levels. Think about armor of agathys and rage with this, if I cast the spell and rage do my temporary hp take half damage from physical attacks?
Yes, they do
Temporary hit points work the same as normal hit points, with the exception that you can't heal them. Resistance or vulnerability is applied to the damage first, and then it applies to your HP, regardless of if it is permanent or temporary HP.
However, there is one thing you need to keep in mind with a warlock/barbarian hybrid and that is that:
If you are able to cast spells, you can't cast them or concentrate on them while raging.
Armor of agathys is not a concentration spell, so this is not a problem for that particular spell, but it is something to keep in mind when you mix a caster and a barbarian.