Seeing Eventide has atmosphere I think both sides of it are going to be warm because of winds - and those are either impulse-like or constant (or so I'm imagining).
Impulse are when light side is getting hotter and hotter, thus air expands more and more and goes to the dark side because of expanding, but, eventually, air on the dark side is so compressed it goes back to the light side (possibly in a explosion-like wave) and gets warmed again and... You know, the cycle repeats.
The second option I've thought is that simply in some places air goes to the dark side, in other goes back and Samarra gives power to this... thing.
I'm saying this because it means Eventide isn't that screwed in either case (since warm distributes itself...) or is screwed even more (...violently).
I'm not sure if I'm right (and possibly I'm not).
And when I've looked at it I thought about something... How shades and mirrors stay in the same place? Shade and one mirror (L1 and L2, respectively) can stay in relatively one place, but others? They would have to orbit the planet and that would probably be a bad thing, as warmed areas wouldn't stay consistent and effects may be marginal, if visible at all. There possibly is a workaround by getting two mirrors in L4 and L5 and letting them shine on the dark side, but that probably wouldn't efficient.
Now that I have thought a bit, if DoM had a sufficiently durable materials they could just link mirrors together and make sure centre of mass is in L2.
After even more overthinking the issue, I concluded tidal lock for a planet with water is a curse because all of water will evaporate and eventually freeze on the cold side, whereas not-locked would have this ice eventually melted by the star.
tl;dr: Eventide is screwed.