I want to make a studio thumbnail but don't want it to appear stretched.

It's 480pixels.
If you do any multiples of it, it will work.

It's inconsistent between parts of the website, if I recall correctly.

here are the sizes studio thumbnails are displayed at in different parts of the website:
homepage: 172x102 (86:51)
my stuff: 100x75 (4:3)
explore page, project page: 204x120 (17:10)
studio page: 300x195 (20:13)

I generally upload studio thumb images at either 170x100 or 340x200