Heat exchange in vacuum largely works with a different principle and is much, much less efficient. Without other molecules to transfer heat to, we're left with black body radiation. Lower efficiency means bigger radiators. It's basically trying to cool down by giving off infrared light.

Something that could be done with a small coolant loop through a river or a glorified AC on earth, requires large sail-like structures in space (sails because it maximizes the surface to throw out that thermal radiation).

Indeed. On top of that, clean water is not that hard to come by with enough energy.

Clean energy is and will be the underlying bottleneck (and no, fusion won't be the answer to that for many more decades; we'll have to solve this long before then).

Wind is not a good option. Just too difficult and slow to set up. Solar could work for electricity in small hospitals and such but hardly much more. It would still take longer to set up than a generator and for hospitals you really want a generator as backup regardless. Solar seems viable for communal centers though.

Heating with electricity is out of the question since resistant heating is the only thing you could set up in time and that's a power hog you really don't want in times of shortages. They might have to do it in some hospitals but it'll be tough on fuel logistics for sure. Coal, wood and fixing the grid asap are the best options for heating.

Germany recently delivered a number of generators from the disaster response teams. I hope those will help.

Yep, seems likely. And this is bad news for everyone since the government has no exit strategy in this.

Giving in or not announcing further lock downs would be a sign of weakness and close to admitting mistakes at this point. Especially after protesters demanded Xi and the party should step down, deescalation seems exceedingly unlikely.

Actually announcing more lock downs though could provoke even fiercer and more widespread protests. People have reached the breaking point it seems. I don't see a way for this to not get ugly.