Final grid:
Solution milestones:
The top row gets us started: both of the two thermometers need to start and end red. That puts a red in the fifth column, increasing the imbalance enough to fill in some there. Purple below means known to be filled, but color not yet known:
The red-labeled columns on the right side together give us the next breakthrough:
and now the middle row has all its greens, which gives a bit more and the rest is straightforward compared to what came before.