Can Heedless Resurrection react to a temporary trigger to kill that temporary unit instead to summon a unit from trash

Yes — you can play Heedless Resurrection in response to the Temporary trigger, kill that Temporary unit as its additional cost, and play a unit from your trash.

Temporary is just a triggered ability that goes on the chain at the start of the beginning phase (Rule 816), and it can be reacted to, putting the game in a Closed state (FAQ #11281, #2751). Because finalization makes you choose the trash target before paying costs, the unit you're bringing back just has to already be in your trash — you can't kill the Temporary unit and then pick that same unit (FAQ #9523). You then kill the Temporary unit as the additional cost; when the Temporary trigger later resolves, its "kill this" has nothing left to act on and does nothing.

One limit to check: the unit you return must cost no more Energy and no more Power than the unit you killed, so if the Temporary unit has a low/no cost that restricts your options.