I've just pushed a fix for this issue. There's now a section on the Gradle preferences page to set Gradle user home and this setting is passed on the tooling API.
However... it looks like the tooling API is buggy in the sense that it only partially obeys the setting.
In my 'custom' user home I see a folder 'caches' and 'daemon' that get created with some stuff in them.
But in my default ~/.gradle folder I am still getting a wrapper folder to which the distributions are getting downloaded.
I don't beleave this is an STS issue but a gradle tooling API issue so will need to take it up with Gradle devs on their forum or bug tracker.