It's not a case of 'heat radiating onto it....from the cold side'.
The foil is a 'low-emissivity' surface; its purpose is to reduce radiant heat transfer from the insulant and in so doing improves the U-value of the element
of which the board forms a part.
Uniform throughout? No gradient?Remember that the foam in the board will attain a certain temperature.
So from the warm side to the cold side?If there was no foil on the cold side, the rough surface of the foam would then emit more radiant heat across the void to the colder side.
Will you please just THINK.its purpose is to reduce radiant heat transfer from the insulant
So not "from the insultant" after all.....The foil on the cold side of the board reduces the emission of radiant heat outwards.
BTW - how much radiant energy makes its way through the plasterboard and decorative finishes which typically are placed over the insulation?