I've been digging around in the site, and it turns out that RedneckDude created a weather gadget that works well enough in objectdock.

https://www.wincustomize.com/explore/desktop_gadgets/307/

Unzip it then put the folder into one of the icon folders in stardock. (you can actually put the folder anywhere in the computer, but if you keep it in the stardock folder, it's easier to save it for a later install)
Then from there, drag and drop the executable file into a space on your objectdock.
It takes a mouseclick to activate the temp, another mouseclick to activate the forecast.

To close, I just right click and select close.