I am writing a scientific thesis and prefer the headings to be set in sans serif. Do humanist or organic sans serif typefaces such as Biolinum work well in this context, in particular if the body font is Palantino?
In pairing a heading face, good design requires either a distinct contrast (a clear and unambiguous differentiation) or a very close family resemblance. Faces with slightly different architecture look like misfits. There are excellent texts that go into this in detail, but probably the most accessible is in Robin Williams' "The Non-Designer's Type Book."
In this case, Biolinum is a bit problematic with Palatino. Both have the thick/thin stroke heritage of pen-drawn characters, but the widths of the characters (you'll see this easily if you compare the lowercase n or h, or the bowls of lowercase d, b and g) and the x-height/cap-height are proportioned differently enough that Biolinum looks a bit squat and out of place.
If you want to use a humanist sans with Palatino, you do have an easy resource. It's very often the case that two typefaces by the same designer look well together. Hermann Zapf designed both Palatino and Optima, and as a result they have enough of a familial relationship that the combination works.
Among non-humanist sans families, Myriad works well with Palatino because the similarity of proportions offsets the contrast of the strokes, so that the heavy contrast doesn't become a visual feature in itself.
An academic paper shouldn't look awkward, nor should it be too overtly "designed." The type should indicate the information hierarchy but otherwise be entirely unobtrusive.
I wouldn't mix Palatino and Biolinum, but that's very subjective. Maybe you could try Akzidenz Grotesk, Avenir or Myriad with Palatino?
P.S.: depends on which field you are wirting your thesis in but are you sure that Palatino has all the Glyphs you need? I'd reconsider this font-choise tbh.