At the end of The Three Body Problem, we discover that the Trisolarans are able to 2-dimensionalize a proton and make it into a computer called a sophon.
The 2-dimensional sophon stretches across the entire sky, wrapping the entire planet and shading it from the stars. From the description it seemed that its mirrored surface would be very protective from electromagnetic radiation. It is capable of becoming more or less transparent so they could tune it how they wished. EDIT: It seems I was wrong about the transparency. I couldn't find the source saying it could become more or less transparent. However, there is another potential solution by stretching it only so far when in 2D mode, and intelligently reflecting light when in a cold era or blocking it during a hot era. Though this would be much easier to explain why this would be difficult or impossible given the nature of the 3-body system since it would have to be more preemptive and the system cannot be predicted.
Once they had created this, couldn't they have just used this sophon to protect them from the harsh environments during Chaotic eras? This seems like it would have solved their survivability problems much more effectively than interaction with the humans.
Note: I have only begun book two so maybe this is addressed later.