I have a unit at 0 or even negative might. When this turn ends, will it be granted any status or keyword like "temporary" that will kill it next turn? Or is its might return to normal when the turn ends?

No. Being at 0 or negative Might doesn't grant any status or keyword — Temporary only applies if a card actually gave the unit Temporary (Rule 816); having low Might never creates it.

At the end of the turn the Expiration Step heals all units and expires every "this turn" effect simultaneously, so the Might modifiers fall off and the unit goes back to its printed/base Might plus any persistent modifiers (attached Gear bonuses, passive abilities) — Rule 317.2.

Also worth separating: 0-or-less Might is never itself lethal. The unit only dies if it has non-zero damage equal to or exceeding its Might (Rule 143.2.a), so a 0-Might unit with no damage simply survives the turn.

The one case where it does die next turn is if it genuinely has Temporary (e.g., a Sprite token) — that trigger kills it at the start of its controller's Beginning Phase before scoring, independent of its Might.