Does temporary generate a trigger?

Yes, the effect of the Temporary keyword triggers and uses the chain.

According to Rule 816.1.b, the Temporary keyword is functionally short for: "At the start of this permanent's controller's Beginning Phase, before scoring, kill this."

Because this is a triggered ability, it follows the standard rules for triggers:

1. Triggering: At the start of the controller's Beginning Phase, the condition is met.
2. Chain: As per RiftJudge FAQ #7456, the resolution of Temporary goes onto the chain as a triggered ability.
3. Interaction: Because it is on the chain, both players have the opportunity to react to it (for example, by playing a [REACTION] card to save the unit, if such an effect is available).

If you do not react to the trigger or the trigger resolves without being stopped, the "kill" instruction will execute, and the unit will be sent to the trash.