Why when we play thermo beam from promising future it linger a chain?

Because Thermo Beam is a Spell, and spells are the only card type that lingers on the Chain. Rule 359.3: "A Spell lingers on the Chain" — it becomes a Finalized Chain Item and waits for the normal resolution step, whereas Units and Gear leave the Chain the instant they're finalized (Rule 337.2). That's why units played from Promising Future hit the board right away but Thermo Beam doesn't.

Promising Future itself doesn't change that behavior — when it tells you to "play" a card mid-resolution, that card just goes on the Chain as a Pending item and its play process pauses (Rule 354.3) until Promising Future fully resolves. After that, Thermo Beam finalizes and sits on the Chain like any other spell until it resolves and goes to trash (Rule 359.3.d). So the "lingering" is normal spell behavior — you'd see exactly the same thing if you played it from your hand.