@jamie @athairbirb A friend of ours once tried this to move hot air from a log burner in an alcove upstairs to their downstairs kitchen.
Although it did work, it wasn't effective in heating the kitchen to any degree of comfort in the end.
They may have out the outlet too high up the kitchen wall perhaps and the heat stayed on the ceiling?
@Jkp The volumetric heat capacity of air is pretty low so you have to move a lot to make much difference to temperature. About 1000 J/kg and 1.25 kg/m³ so to move 1 kWh (3.6 MJ) at a temperature difference of 10 °C you have to move 3.6e6 / (1000 * 1.25 * 10) = 288 m³.
@jamie Can you temporarily shade the front of your shed? Try to deal with the source of the problem rather than the symptoms.
@edavies Thanks. I knew there would be a sciency answer! The shed is very small, and a small duct fan can allegedly move 100m3 an hour, which sounds like it should make some difference by those figures - but I think you're right, an awning or something to keep the sun off the walls might be more practical.