Can I play a hidden card at my beginning phase before my shadow call procs?

Yes — you can play a Hidden card in response to Temporary's death trigger, before it resolves and kills your unit.

Here's the timing breakdown:

1. Your Beginning Phase begins with the Beginning Step (Rule 315.2.a). Just the phase starting does not create a reaction window — you cannot play anything yet.

2. Temporary's trigger (Rule 816) immediately goes on the Chain as a Pending Item — "At the start of this permanent's controller's Beginning Phase, before scoring, kill this." This creates a Closed State (Rule 401.1).

3. Now there's a Chain, so you have a reaction window. Your Hidden card has Reaction while facedown (Rule 811.6), so you can play it here in response to the trigger — before the kill resolves.

So the answer is yes, as long as you didn't hide the card on the same turn (Hidden cannot be played the turn it was hidden per FAQ #8114). Wait for the Temporary trigger to go on the Chain, then respond with your Hidden card.