How to set ToolTip position?

[igor_stravinsky]

The docs say "The position of the shared tool tip is determined by the framework.", but I'd like to get the tool tip closer to the button it corresponds to:

In this case the ToolTip looks like it's associated with the button above the Temperature, and I'd like to move it down so it appears just above the bottom button.

Attempts to change the margin, padding, x and y positions have all failed. I guess the ultimate solution is to write my own ToolTip, but I'd like to avoid that if possible.