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Neither of those options (AIRFLOWNETWORK:MULTIZONE:COMPONENT:HORIZONTALOPENING or ZONECROSSMIXING) will give you a result that is particularly meaningful in isolation. I'm not sure what you mean by "CFD but it is not applicable in this case since we want to control to openings of the atrium, at the top floor, based on the temperature", but for the mixing object you'll need flow rates and I've written more answers here than I care to think about on why AirflowNetwork is not a great choice for subdividing large volumes.
If you know what the flow rates are (not sure how that's possible without CFD) or you can determine the model parameters that AirflowNetwork will need (also not sure how that's possible without CFD) then either path could be made to work. But neither path will give you a result that you can be confident in without pre-simulation knowledge of what the flow patterns should look like (which should be available from CFD).