Fill the thermometers with mercury, such that the numbers outside the grid indicate how many cells in each row and column are filled. Mercury always starts filling from the base (circular part) of a thermometer, towards the top. This does not depend on the actual orientation of the thermometer (some are upside down).
The top row needs to have three filled cells. Since there is only one thermometer in this row, the first three cells of it have to be filled (the leftmost three cells). Now, in the leftmost column, one cell is already full, so two more have to be filled. Again, there is onlty one thermometer remaining in this column, so we know the bottom two cells of this thermometer have to be used.
Now, the third row already has its filled cell, which means that the resst of this row stays empty. Because the bottom right thermometer has an empty base, it must be completely empty. Therefore, int he last column, there is now only one spot left. The bottom row is also clear, and finally the last cell to be filled must be in the third column and second row.