'Part shade' can mean anything, Scottish. I like the SRGC idea that here, in Scotland, all our gardens can be considered to be in part shade because of our geographical position. In most years we only get a few days of scorching weather, when the corms are dormant anyway.
They self-seed around our garden and are growing happily in full sun, part shade and even more shade. The leaves will die back in spring (wonderful foliage through the winter) and then reapear after the flowers in early autumn.

I've seen them under really big mature trees.

I have some in really deep shade, and they're still happy and flower every year

Yep, really deep shade for me

And this year seems to have a good year for them. Everywhere under garden hedges, escaped into field edges, and in almost any situation. I went to a garden the other day where the owner had found all these 'fungi' in his garden and had dug them all up to throw away. Some of the corms (for that's what they were) were 8 inches across or more. I managed to salvage a few!

I have them in deep shade under the beech tree. and yes they do lose their leaves during the summer.

Thanks everyone - pleased to read they will cope with more shade than I expected.
Bulba - had a similar comment made to me recently when I commented on how well some shade lovers cope with in the sunniest situations in my garden. Full Sun in Scotland...not very often ;)
Hortum cret - great find! One man's treasure and all that!