There are several hundred species of
Disa, but you're most likely to come across
D. uniflora or it's hybrids. I find them very finicky plants that like to keel over. In the wild, they do sometimes experience very hot weather, but they usually grow right next to streams with their roots (and often leaves) in the shade - and the roots are cooled and bathed by the icy streams.
I saw somewhere on the internet someone who had modified a chest freezer to cool down water, which was then intermittently pumped into the
Disa growing container above - this was somewhere in the USA where it's rather hot, and it looked like it worked well. Ah,
here it is.
I suspect if you keep the roots cool and moist (and they don't have day in day out baking hot, dry conditions) all will be well.
They seem to do best in sphagnum.
I imagine that the
"cool stretching" idea on Ray's site might help too, but as I haven't managed to get suitable substrates to try it, I haven't.
Do let us know how your plant does, as I was also wondering how
Disa would do in S/H!