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"I've heard that a lubricant's life is cut in half for every 10 degrees C (18 degrees F) increase in operating temperature. Is there any truth to this?"
Yes, this is generally true. The concept is based on the Arrhenius equation, named for 19th-century Swedish chemist Svante Arrhenius. In 1903, Arrhenius won a Nobel Prize when he figured out the relationship between temperature and most chemical reaction rates. Often called the Arrhenius Rate Rule, it relates to the fact that lubricants, once they've exceeded their base activation temperature, will degrade (oxidize) twice as fast for every 10 degrees C (18 degrees F) increase in temperature. In fact, there are a range of problems associated with too much heat, such as:
Heat increases both the collision rate of molecules and the activation energy of the reaction. The higher activation energy helps overcome the barrier (or natural resistance) molecules have to chemical reactions.
With oils, the chemical reaction that typically causes base oil degradation and additive depletion is oxidation. The activation energy required to induce oxidation in oil is high compared to other chemical reactions. The presence of contaminants such as water and certain metal particles in the oil can considerably speed up the process, thus increasing the activation rate. For most in-service mineral oils with typical contaminants, the activation energy for oxidation corresponds to a doubling for every 10 degrees C temperature increment.
Why does a refrigerator keep food from spoiling? Spoiling is a chemical reaction like oil oxidation but proceeds at a much higher rate constant. Compared to a refrigerator (4 degrees F), food will spoil at a rate 142 times faster at room temperature (77 degrees F). In other words, the speed of reaction in a freezer is much slower than at room temperature.
So what happens if you let the oil degrade? The eventual breakdown of the molecules is inevitable. It can be prolonged by keeping the oil clean, cool and dry, but it will eventually happen. When it does, the byproducts of the reaction are harmful for machine health.
First to form are carboxylic acids. These acids are relatively weak, but they can start to corrode machine surfaces if left in a system for a great deal of time. Left unchecked, the now heavily oxidized oil will start to form sludge and varnish. This sludge and varnish can cause filter plugging, blockage of critical oil clearances, valve stiction and many other precursors to machinery failure.