[Terrysch]

Cutting oil keeps the temperature down, not increases it.
But a drop will not do that. When you look at machining, the cutting fluid is pouring on the tool and cutting piece to wash away the chips and cool.

There is some new high tech cutting fluids, that do only use a mist. Keeps the machining chips cleaner so worth more as scrap, plus reduces amount of cutting oil purchased and used, which is expensive - oil!!!!!.
But they are only for aluminum - aerospace especially.

I am retired mechanical engineer who worked most of my career at John Deere and Mercury Marine with background in machining steel and aluminum.