The temp. is now 31.6°C! I think the problem must be elsewhere - eg bad insulation under the roof tiles, although I don't get the impression that the walls and ceiling are 30°!
The Al foil is quite hot on the inside; ...
I didn’t expect that.
A bit of websearching reveals some practical engineering knowledge: that high albedo – reflecting light – is not the only quality needed by a material to prevent heating by sunlight through a window. The material also needs to have a high heat emissivity, to emit absorbed visible light as infrared light, rather than reaching a high surface temperature, which heats the surrounding air via convection.
I found a chart titled “Spectral characteristics of building materials” at this energy utility trade website
. It is about roof, not window shade material, but I think the principles apply to both.
Notice that while “polished aluminum foil” has a high albedo (“solar reflectance” in the diagram) of 0.85 to 0.95, its “far-infrared emissivity” is low, 0.05. This explains why aluminum foil gets hot, and perhaps does more to convectively heat the room than it does to cool it by reflecting incoming light.
... would it make any difference if the foil was fixed outside on the window, ie OVER the glass window?
Yes, I expect it would make a big difference, as the hot aluminum foil would then be heating air on the outside of the window, not the inside.
Also, glass is less transparent in the infrared spectrum than in the visible (source: commercial webpage “Measurement of Solar Transmittance through Plate Glass”
), so much of the infrared light radiated by the foil will be kept on the side of the glass the foil is on.
Since it’s usually easier to hang stuff inside a window than outside, maybe you should keep your shield on the inside, but switch to a high albedo/high emissivity material. On the diagram, “white plaster” is highest for both of these – my guess is a piece of white sheetrock would be good. If you don’t have that handy, I’d try white paper.