I’ve once used cooking oil as a thermal paste substitute. Worked well enough and nothing went wrong.
I'm more worried that the oil won't get to a high enough temperature and thus won't polymerize, so it'll flow out and ruin some other component, or go rancid, or something. Thermal paste won't move on you. Oil will.
https://www.pugetsystems.com/submerged.php as an example.
Pretty much any Solid-liquid-solid or solid-solid-solid interface will be better than solid-roomTemp&Pressure gas-solid.
The whole point is to conduct heat better than air, and most things will.