When my opponent plays Promising Future and reveals dazzling aurora, can I reveal thermobeam to destroy it, or will it resolve in such order that aurora will be played after thermobeam resolves?

Yes — a Thermo Beam played through Promising Future will kill Dazzling Aurora, but Aurora still enters play first. There is no response window to a permanent being played: gears and units finalize immediately and leave the chain (Rule 359.2), so you can't destroy it "before it's played."

Here's the order: "starting with the next player," you play first. Thermo Beam goes on the chain first but, as a spell, lingers as a finalized item while Aurora (a permanent) finalizes and enters play — then Thermo Beam resolves and kills all gear, Aurora included (Rule 359.3.b). Timing isn't an obstacle either: cards played as part of an effect like Promising Future ignore normal Action/Reaction timing restrictions (RiftJudge FAQ #4658). If you instead meant playing Thermo Beam from hand in response — that isn't possible: it's Action speed and permanents don't linger on the chain for reactions.