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Well, the only question I found in this website about volumetric displays on air was this one, but it specifically suggests making air denser in order to make it work, but my question is specifically about changing the temperature of air to show the voxels.

In other words, the intention is to heat a portion of air (a cubic shaped area of any size) with simple jet of hot air or using a lot of lasers for it, and then pointing a projector or RBG lasers to convey in specific points, (supposedly) making voxels.

Like pointing a laser to a mirage that appeared above a hot area, you would (supposedly) see the laser path.

How hot I would need to this cube of air to be in order to refract the lasers/projectors light?

Or it would be better to heat small points and then throw the lasers/projector at it, since it would be unsafe/uncomfortable to be around a continuous jet of hot air?

The closest thing I could find was that volumetric display that ionises air with lasers to create images with points of light (but I think it is too dangerous to mess with it, maybe it can blind someone if you're not careful?) and the Heliodisplay, that throws a jet of condensed air/steam to project a image on it.

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To do what you are suggesting would require changing the index of refraction of the air significantly by heating and cooling localized points in space. The temperature dependence of the index of refraction of air has been addressed in another physics stackexchange post: Refractive Index of Air Depending on Temperature. It gives an equation that may be useful for your query.

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