The third floor in my house is a single room that has 2 small AC registers near the floor because there is no way to route the duct work to the ceiling. There are no intake vents. In the summer, the room get very warm because warm air gets trapped. An AC guy recently installed a booster fan to one of the ducts to push more cold air, and the room is definitely cooler, but I'm hoping we can do more.

The AC guy said he could install an intake valve on the wall right above that same register that's boosted since there's a little room, but I'm dubious about how much that would improve things. Instead, is there a way to push warm air directly out from the room to the outside, i.e., near the ceiling?

i think i would just grab a small standalone a/c unit and run that when you want it cool. instead of going through the trouble of making other changes.

assuming of course you have a window to vent it out of in that room.

Agree with the window AC, even a through-the-wall AC solution ... complicated if no exterior walls (only attic for venting out).

It would be only second best a solution to continue to attempt satisfaction using the main central HVAC solution if heating is adequate via that avenue. Assuming there's no thermostat/controls to make 3rd floor comfortable. The solution less satisfactory to the windows AC would be to mount a high wall return air aka "intake vent", then duct it on exterior wall, through roof & attic down to main RA trunk. Now it needs insulation & siding.
Can you confirm this was a spec.house build?

Transfer fan

What do you mean "sealed".

I've seen doors that don't allow air to escape because of a tight fit at the bottom and just trimmed some off of the bottom.

You mentioned a fan in the ceiling, which could be accomplished by a bathroom fart fan.

Sorry, by sealed I just meant it's a stand-alone room with windows and ceiling but no attic that is reachable. The idea of adding an intake there the top of the room with attached duct column on the outside is interesting. I think the suggestion of putting a simple window AC unit may be the most practical, esp since we don't use the room that often. Thanks all!

Rather than a window unit, I would consider a mini split. Have lived with a couple of them and they have been fantastic.

Independence H-D said:

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Rather than a window unit, I would consider a mini split. Have lived with a couple of them and they have been fantastic.

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What is a mini split?

https://www.alpinehomeair.com/product/air-conditioning-cooling/ductless-mini-splits/single-zone-mini-split-systems/blueridge/bm09y22?linkfrom=froogle&campaign=61108680&content=6279207960&keyword=453077954&gad_source=1&gclid=CjwKCAjwmrqzBhAoEiwAXVpgoi5RIdD8YL5f2x1buZ8aDSPfegLQ7PG7Yg6WFeqpuprUm7o66tF7ExoCApAQAvD_BwE

Here's mine in my office/studio.