In preparing a surface for paint / glue / thermal paste / soldering / whatever, there is one thing to remember. A normal finger print is of similar thickness to cling wrap (0.01mm). A thick (eg post pizza) print, where the ridges are no longer visible, is closer to the thickness of a sheet of paper (0.1mm).
Rule of thumb. If you would you would not be happy with this kind of material on the surface of whatever you are coating, remove your finger prints.