does mirror image give the unit chosen temporary?

No — Mirror Image grants Temporary to the Reflection token it creates, not to the unit you chose.

The spell reads "Choose a unit. Play a ready Reflection unit token... It becomes a copy of that unit. Give it [Temporary]." The "it" refers to the Reflection token, so only the copy gets Temporary and is killed at the start of its controller's next Beginning Phase (Rule 816.1.b). The original chosen unit keeps whatever it had and is completely unaffected by the spell. This is also why a Reflection token that fails to copy (e.g. the target left the board) still has Temporary — it comes from the spell's own grant (FAQ #11492).