All movements are susceptible to changes of temperature and quartz is no exception.

To expand on this (and this is my layperson's understanding, subject to layperson's error): In a typical quartz movement, a quartz crystal is exposed to current, and vibrates at 32.768 kHz (or 32,768 vibrations per second). A microprocessor counts the number of vibrations, and registers a "tick" of the second hand for every 32,768 vibrations counted. (This assumes it's an analog watch; for digital, the same principle applies, only the elapsed second is registered on the display, rather than via a hand). The problem is that the frequency at which a quartz crystal vibrates varies with temperature. So, if the temperature causes the crystal to vibrate more slowly, it will take longer for the processor to register the 32,768 vibrations, meaning a "second" actually takes longer than a second; and vice versa for temperatures causing the crystal to vibrate at a faster rate. In a standard quartz movement, the microprocessor doesn't know the difference - it counts 32,768, whether it takes exactly a second, or less, or more. In a typical thermocompensated quartz movement (there are actually different methods of thermocompensation), there is additional circuitry that measures the temperature, calculates how much more slowly or quickly the crystal is vibrating per second than the standard rate, and adjusts the required number of vibrations to advance the second hand. That's the long and the short of it. For a much more in-depth explanation, see this excellent, but lengthy, writeup on WUS.

I have to wonder how necessary thermocompensation is. In theory, it's awesome technology. Given the relative rarity of COSC certified quartz movements, Breitling's Superquartz has a cachet all its own. However, I have a basic quartz TAG that is typically accurate to within 1-2 seconds a month, which is almost on a level with thermocompensated quartz. Maybe that's not typical, and I just got lucky with a particularly good specimen of a movement. Or it could be that the circumstances in which I wear it just don't present enough temperature variation to make a huge difference in accuracy. Perhaps in more extreme uses, I'd see a bigger variance. Which leads back to my question: how helpful is thermocompensation for the average watch wearer? Does one need to be in the elements on a regular basis for it to really make much of a difference?