Well, your watch at any rate.
Temperature compensating balances, low thermal expansion alloys, the problem of rate change due to temperature has been known for some time, and ways to counter it are actually pretty well understood.
But, how bad does it get? I mean for the average watch we have today?
Very few, if anybody, used an active temperature compensation system these days, too expensive and time consuming to adjust. No, the passive low thermal expansion alloy is the system of choice. This actually makes answering the question easier.
There are about five or six alloys out there used for balance springs, all are some form of cobalt-nickel-chromium alloy. The better known alloys are the proprietary alloys of Nivarox, Anachron (Nivarox, part of SWATCH), Parachrom (Rolex) and SPRON (Seiko). How good are these alloys at compensating for temperature (or, more correctly, not allowing temperature to affect them.)
We know that the limits for temperature variation set forth by ISO 3159, the specifications for chronometers is +/- 0.6 s/d/degree C for watches over 20 mm in diameter and +/- 0.7 s/d/degree C for watches equal to or under 20 mm. We also know that watches with the above mentioned alloys are capable of meeting these limits without resorting to other, fancier measures. So, we can conclude that the thermal expansion of the various alloys is sufficiently small that it alone can limit rate change due to temperature to 0.6 s/d/C.
How many seconds per day will that be?
Let us assume the watch was regulated in a cozy room with the thermostat set at 22 deg C, then worn 1) in the desert at 49 deg C, and 2) in the mountains at -10 deg C.
1) The temperature change in this case is 27 deg C, for ease of calculation let’s round the rate change to 1/2 s/d/C, so the watch in this case will slow 13.5 s/d from its original regulated rate.
2) The temperature change in this case is 32 deg C, so the watch will increase its rate by 16 s/d.
A watch worn on the wrist will eventually reach some temperature that is near skin temperature, maybe 32-33 deg C, so an argument can be made that wearing the watch all the time will aid in the stability of the rate over removing it at night (and allowing it to cool down).
What about quartz?
I should just refer you to that 8,000 word novella by Bruce Reding over on the High Accuracy Quartz forum, but I will sum it up for the general, non-compensated quartz.
First, the quality of the quartz crystal matters, the AT cut (it has to do with the orientation of the cut to the geometry of the crystal structure, see Figure 1) is the most used in watch due to the flat section around 25 deg C, seen in Figure 2.
In Figure 3, however, you see that cutting errors (expressed in degrees off zero) result in more pronounced “waviness”.
Fig. 1) Orientation angle of a Z-plate quartz crystal
Figure 2. Change in Frequency v. Temperature
Figure 3. Change in Frequency v. Temperature v. Cut Angle
In the case of a watch quartz operating at 32768 Hz, 50 PPM (parts per million) is about 4.32 sec/day. So a well cut quartz crystal (0 deg) should stay within +/- 1 sec/day in a temperature range from -20 to +80 deg C. A poorly cut one could vary as much as +/- 10 seconds over a similar temperature range.
All quartz are not equal......