Also, keep in mind that refrigerators cycle on and off. A standard refrigeration compressor cannot be cycled too quickly or the valves will be damaged by liquid. Once the compressor cycles off, you must let it remain off for, perhaps, ten minutes before you can safely cycle it back on.
And the more often you cycle the compressor on and off, the faster things wear out, and the less energy efficient the system is.
So typical refrigerators and freezers cycle up and down in temperature. How much depends on the particular fridge or freezer, but having set up hundreds of them in laboratories with continuous temperature monitoring and logging, I can tell you that a fifteen degree temperature swing in a home-style freezer is not uncommon. Refrigerators are not as bad, but still pretty bad.
Further, due to the lack of active stirring of the air in a typical home fridge or freezer, the temperature can vary from place to place (even inches apart!). This is also true in ovens, incubators, etc. The air is stagnant and not stirred, so it stratifies and you can have wide variations in temperature over fairly short distances.
And, since every probe you put in the fridge will have a different thermal time constant, what any given probe reads at any moment in time will depend on the rate at which the air around it is changing temperature and the speed of response of that particular probe. When you see this plotted on a graph in a data-logging system, you see a phase and amplitude difference between different probes placed in the same location.
In other words, the graphs made by several different probes, all perfectly calibrated, do NOT lay on top of each other. They may all report the same average temperature when averaged over an hour or so, but at any given moment, they will disagree, and perhaps by ten or more degrees, even though they're all very accurate probes.
What is commonly done for refrigerator thermometers in a laboratory is to have a container filled with a glycol or other solution into which the thermometer's measuring bulb is placed. That way, when you whip the fridge door open and read the thermometer, it won't immediately start changing temperature before you can get your reading.
The same kind of thing can be done when comparing temperature probes. Ideally, you'll have a stirred, temperature controlled water bath, or a "dry block calibrator" that employs an aluminum or copper block with holes in it for the probes such that they're all held at a similar temperature by virtue of the high thermal conductivity of the aluminum or copper. The stirred water bath is, however, the most precise.
Still, just putting all of your sensors into a cup of water, hopefully with all of their sensitive areas held close to each other with a rubber band or the like, and then putting that cup of water into the fridge will let you see what they all think of that fridge's temperature over an average of time determined by the thermal time constant of that cup of water.
For testing at the ice point of water, you should prepare your ice bath as an "ice slush" with the ice particles "the consistency of a snow cone" (according to NIST). And the water and ice should be made using distilled water. Further, you must drain off excess water as the ice slush melts so that you have no areas that are flooded with only liquid water. Likewise, you don't want any "dry" areas of only ice particles.
Distilled or deionized water is best because dissolved salts or other things can raise or lower the freezing point. Don't even let your fingers touch the slush as the salt from your hands can lower the freezing point measurably. At least rinse your hands very well, and ideally, wear disposable rubber gloves when handling your probes and the ice slush.
The problem with ice cubes is that freezers are, naturally, kept well below freezing to assure that they actually freeze things. So the cubes will be well below freezing, too, for quite some time. If the probe tip touches an ice cube, it will read the colder-than-freezing temperature of that cube. And if the probe tip is out in a large area of liquid water between these large cubes, then it will read a warmer temperature because that water is not in intimate contact with any of the ice.
Using a slush of "snowcone consistency" that is not too watery, yet not at all dry, assures that the ice particles and the water are all in very intimate contact everywhere. The distances are small, so the liquid water and the ice particles all equilibrate to the same temperature very quickly. And then, no matter where the sensitive part of the probe is placed, it will "see" the exact melting point of the ice.
If you do all of that, the accuracy of an ice slush is fantastic. Well within 1/100th of a degree C!
For boiling water, you do need to use an altitude versus boiling point chart. NEVER use the barometer reading provided by weather reporters or websites since they use the "corrected to sea level" barometer reading. What you need is the "station pressure", which will be, of course, much lower as you go up in elevation.
Scroll down to the chart found here:
http://www.engineeringtoolbox.com/boiling-points-water-altitude-d_1344.html
I saw an inaccurate chart posted on this site somewhere just a few minutes ago! This one is correct.
As for the safety of the probes: As has been said, it depends on the type of probe. Some are waterproof, some are not. A "not waterproof" probe can be placed into one of those thin, disposable plastic sanitary sleeves they sell in the pharmacy department of your local Wal Mart or drug store to put over fever thermometers to prevent the spread of germs. Then stick that down into the ice slush. It will slow the response of the sensor, but if you stick it in deep enough, it will eventually report the correct temperature.
