So recently I've been putting olive oil in a spoon floating in boiling water in a metal dish so that it gets warm enough to put in my ears. I assume the oil will warm as the water transfers heat to it, then cool as the water cools, (or at the very least is not transferring enough energy to the oil to outweigh the rate at which the oil loses heat energy) but I don't know how to predict when the oil will hit its warmest temperature.

 

I figure I could one day set aside the spoon and put a thermometer in boiling water in a metal dish (though I keep forgetting to buy an actual themometer) to gauge how long it would take to cool without having to heat up the olive oil at the same time. However, I'm also wondering... is it possible that instead of cooling slower, the water cools faster, as there's no spoon or olive oil to "insulate" the temperature drop? What factors would need to be taken into consideration in determining how long it takes to max out in temperature, and how that differs between with or without a spoon with olive oil?

No.  The rate at which a substance cools is proportional to the difference in tempature between the substance and the atmosphere.  For one thng, metal (or oliive oil) is not a good insulator.  For another, the size of the spoon is very small compared to the surface area of the pot the water is in.

What if I had a smaller dish (ie. 1/4 cup metallic measuring cup) in which to put the hot water? Could the effect of covering most of the top surface with a spoon almost as large as the top surface, and filling the spoon with olive oil, still be considered negligible then?