Others could explain it better than I can, and maybe someone with more expertise will chime in. This topic gets pretty regularly discussed, and just like the evaporation of mixed liquid stove fuels in pressurized canisters, it sometimes attracts some good technical explanations.
The only theoretical foundation you need is this: every material absorbs and emits radiant heat to some unique extent, and, in general, materials that are good at reflecting heat are bad at emitting it. Aluminum foil is very good at reflecting heat, so it is bad at emitting it. If a flat object (a brim of a hat, say) has shiny aluminum on both sides, and is turned to face the sun, the sunlit side will reflect most of the heat, and the shaded side will hardly emit any of the small amount of heat absorbed by the sunlit side. So the head under the hat gets almost no radiant heat. If the brim was aluminum above and dark fabric below, the top would reflect and the bottom would emit onto the wearer much more of the small amount of heat absorbed by the top side, because dark organic materials (like darkly colored plastics) are very good at emitting radiant heat.
If you are considering materials for your project, the property I described above is related to a quantity called emissivity. If the emissivity of a material is low (like aluminum), then it doesn’t absorb or emit very much radiant heat. If the emissivity is high (like plastics, asphalt, and water), then it absorbs a lot of radiant heat and emits a lot. For your project, you want the upper and lower surfaces to have low emissivity, like the aluminum surface of a space blanket, not high emissivity, like dark fabric.
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